X² = ((3-1.05)²)/1.05+ ((7-8.50)²)/8.50+((0-0.46)²)/0.46+((6-7.63)²)/7.63+((64-62.03)²)/62.03+((3-3.34)²)/3.34+((4-4.08)²)/4.08+((33-33.13)²)/33.13+((2-1.78)²)/1.78+((0-0.42)²)/0.42+((3-3.40)²)/3.40+((1-0.18)²)/0.18+((3-2.82)²)/2.82+((23-22.92)²)/22.92+((1-1.24)²)/1.24

asked by guest
on Jan 14, 2025 at 7:09 am



You asked:

Solve the equation X2=(3−1.05)21.05+(7−8.50)28.50+(0−0.46)20.46+(6−7.63)27.63+(64−62.03)262.03+(3−3.34)23.34+(4−4.08)24.08+(33−33.13)233.13+(2−1.78)21.78+(0−0.42)20.42+(3−3.40)23.40+(1−0.18)20.18+(3−2.82)22.82+(23−22.92)222.92+(1−1.24)21.24{X}^{2} = \frac{{\left( 3 - 1.05 \right)}^{2}}{1.05} + \frac{{\left( 7 - 8.50 \right)}^{2}}{8.50} + \frac{{\left( 0 - 0.46 \right)}^{2}}{0.46} + \frac{{\left( 6 - 7.63 \right)}^{2}}{7.63} + \frac{{\left( 64 - 62.03 \right)}^{2}}{62.03} + \frac{{\left( 3 - 3.34 \right)}^{2}}{3.34} + \frac{{\left( 4 - 4.08 \right)}^{2}}{4.08} + \frac{{\left( 33 - 33.13 \right)}^{2}}{33.13} + \frac{{\left( 2 - 1.78 \right)}^{2}}{1.78} + \frac{{\left( 0 - 0.42 \right)}^{2}}{0.42} + \frac{{\left( 3 - 3.40 \right)}^{2}}{3.40} + \frac{{\left( 1 - 0.18 \right)}^{2}}{0.18} + \frac{{\left( 3 - 2.82 \right)}^{2}}{2.82} + \frac{{\left( 23 - 22.92 \right)}^{2}}{22.92} + \frac{{\left( 1 - 1.24 \right)}^{2}}{1.24} for the variable XX.

MathBot Answer:

X=343795916268288311044661117464851089966223981945666523041161570510≈3.0135746X=−343795916268288311044661117464851089966223981945666523041161570510≈−3.0135746\begin{aligned}X &= \frac{\sqrt{34379591626828831104466111746485108996622398}}{1945666523041161570510} \approx 3.0135746\\X &= - \frac{\sqrt{34379591626828831104466111746485108996622398}}{1945666523041161570510} \approx -3.0135746\end{aligned}

Take the square root of both sides of the equation X2=(23−(92⋅1100+22))292⋅1100+22+(33−(13⋅1100+33))213⋅1100+33+(4−(8⋅1100+4))28⋅1100+4+(3−(82⋅1100+2))282⋅1100+2+(2−(78⋅1100+1))278⋅1100+1+(3−(34⋅1100+3))234⋅1100+3+(1−(24⋅1100+1))224⋅1100+1+(3−(4⋅110+3))24⋅110+3+(64−(3⋅1100+62))23⋅1100+62+(7−(5⋅110+8))25⋅110+8+(6−(63⋅1100+7))263⋅1100+7+(−42100+0)21100⋅42+(−46100+0)21100⋅46+(3−(5⋅1100+1))25⋅1100+1+(1−18⋅1100)21100⋅18X2=(23−(92⋅1100+22))292⋅1100+22+(33−(13⋅1100+33))213⋅1100+33+(4−(8⋅1100+4))28⋅1100+4+(3−(82⋅1100+2))282⋅1100+2+(2−(78⋅1100+1))278⋅1100+1+(3−(34⋅1100+3))234⋅1100+3+(1−(24⋅1100+1))224⋅1100+1+(3−(4⋅110+3))24⋅110+3+(64−(3⋅1100+62))23⋅1100+62+(7−(5⋅110+8))25⋅110+8+(6−(63⋅1100+7))263⋅1100+7+(−42100+0)21100⋅42+(−46100+0)21100⋅46+(3−(5⋅1100+1))25⋅1100+1+(1−18⋅1100)21100⋅18\begin{aligned}X^{2} &= \frac{\left(23 - \left(92 \cdot \frac{1}{100} + 22\right)\right)^{2}}{92 \cdot \frac{1}{100} + 22} + \frac{\left(33 - \left(13 \cdot \frac{1}{100} + 33\right)\right)^{2}}{13 \cdot \frac{1}{100} + 33} + \frac{\left(4 - \left(8 \cdot \frac{1}{100} + 4\right)\right)^{2}}{8 \cdot \frac{1}{100} + 4} + \frac{\left(3 - \left(82 \cdot \frac{1}{100} + 2\right)\right)^{2}}{82 \cdot \frac{1}{100} + 2} + \frac{\left(2 - \left(78 \cdot \frac{1}{100} + 1\right)\right)^{2}}{78 \cdot \frac{1}{100} + 1} + \frac{\left(3 - \left(34 \cdot \frac{1}{100} + 3\right)\right)^{2}}{34 \cdot \frac{1}{100} + 3} + \frac{\left(1 - \left(24 \cdot \frac{1}{100} + 1\right)\right)^{2}}{24 \cdot \frac{1}{100} + 1} + \frac{\left(3 - \left(4 \cdot \frac{1}{10} + 3\right)\right)^{2}}{4 \cdot \frac{1}{10} + 3} + \frac{\left(64 - \left(3 \cdot \frac{1}{100} + 62\right)\right)^{2}}{3 \cdot \frac{1}{100} + 62} + \frac{\left(7 - \left(5 \cdot \frac{1}{10} + 8\right)\right)^{2}}{5 \cdot \frac{1}{10} + 8} + \frac{\left(6 - \left(63 \cdot \frac{1}{100} + 7\right)\right)^{2}}{63 \cdot \frac{1}{100} + 7} + \frac{\left(- \frac{42}{100} + 0\right)^{2}}{\frac{1}{100} \cdot 42} + \frac{\left(- \frac{46}{100} + 0\right)^{2}}{\frac{1}{100} \cdot 46} + \frac{\left(3 - \left(5 \cdot \frac{1}{100} + 1\right)\right)^{2}}{5 \cdot \frac{1}{100} + 1} + \frac{\left(1 - 18 \cdot \frac{1}{100}\right)^{2}}{\frac{1}{100} \cdot 18} \\ \sqrt{X^{2}} &= \sqrt{\frac{\left(23 - \left(92 \cdot \frac{1}{100} + 22\right)\right)^{2}}{92 \cdot \frac{1}{100} + 22} + \frac{\left(33 - \left(13 \cdot \frac{1}{100} + 33\right)\right)^{2}}{13 \cdot \frac{1}{100} + 33} + \frac{\left(4 - \left(8 \cdot \frac{1}{100} + 4\right)\right)^{2}}{8 \cdot \frac{1}{100} + 4} + \frac{\left(3 - \left(82 \cdot \frac{1}{100} + 2\right)\right)^{2}}{82 \cdot \frac{1}{100} + 2} + \frac{\left(2 - \left(78 \cdot \frac{1}{100} + 1\right)\right)^{2}}{78 \cdot \frac{1}{100} + 1} + \frac{\left(3 - \left(34 \cdot \frac{1}{100} + 3\right)\right)^{2}}{34 \cdot \frac{1}{100} + 3} + \frac{\left(1 - \left(24 \cdot \frac{1}{100} + 1\right)\right)^{2}}{24 \cdot \frac{1}{100} + 1} + \frac{\left(3 - \left(4 \cdot \frac{1}{10} + 3\right)\right)^{2}}{4 \cdot \frac{1}{10} + 3} + \frac{\left(64 - \left(3 \cdot \frac{1}{100} + 62\right)\right)^{2}}{3 \cdot \frac{1}{100} + 62} + \frac{\left(7 - \left(5 \cdot \frac{1}{10} + 8\right)\right)^{2}}{5 \cdot \frac{1}{10} + 8} + \frac{\left(6 - \left(63 \cdot \frac{1}{100} + 7\right)\right)^{2}}{63 \cdot \frac{1}{100} + 7} + \frac{\left(- \frac{42}{100} + 0\right)^{2}}{\frac{1}{100} \cdot 42} + \frac{\left(- \frac{46}{100} + 0\right)^{2}}{\frac{1}{100} \cdot 46} + \frac{\left(3 - \left(5 \cdot \frac{1}{100} + 1\right)\right)^{2}}{5 \cdot \frac{1}{100} + 1} + \frac{\left(1 - 18 \cdot \frac{1}{100}\right)^{2}}{\frac{1}{100} \cdot 18}} \end{aligned}

Remember that both positive and negative numbers will result in a positive number when squared, so a square root will have both a positive and a negative answer. X=±(23−(92⋅1100+22))292⋅1100+22+(33−(13⋅1100+33))213⋅1100+33+(4−(8⋅1100+4))28⋅1100+4+(3−(82⋅1100+2))282⋅1100+2+(2−(78⋅1100+1))278⋅1100+1+(3−(34⋅1100+3))234⋅1100+3+(1−(24⋅1100+1))224⋅1100+1+(3−(4⋅110+3))24⋅110+3+(64−(3⋅1100+62))23⋅1100+62+(7−(5⋅110+8))25⋅110+8+(6−(63⋅1100+7))263⋅1100+7+(−42100+0)21100⋅42+(−46100+0)21100⋅46+(3−(5⋅1100+1))25⋅1100+1+(1−18⋅1100)21100⋅18X=(23−(92⋅1100+22))292⋅1100+22+(33−(13⋅1100+33))213⋅1100+33+(4−(8⋅1100+4))28⋅1100+4+(3−(82⋅1100+2))282⋅1100+2+(2−(78⋅1100+1))278⋅1100+1+(3−(34⋅1100+3))234⋅1100+3+(1−(24⋅1100+1))224⋅1100+1+(3−(4⋅110+3))24⋅110+3+(64−(3⋅1100+62))23⋅1100+62+(7−(5⋅110+8))25⋅110+8+(6−(63⋅1100+7))263⋅1100+7+(−42100+0)21100⋅42+(−46100+0)21100⋅46+(3−(5⋅1100+1))25⋅1100+1+(1−18⋅1100)21100⋅18, X=−(23−(92⋅1100+22))292⋅1100+22+(33−(13⋅1100+33))213⋅1100+33+(4−(8⋅1100+4))28⋅1100+4+(3−(82⋅1100+2))282⋅1100+2+(2−(78⋅1100+1))278⋅1100+1+(3−(34⋅1100+3))234⋅1100+3+(1−(24⋅1100+1))224⋅1100+1+(3−(4⋅110+3))24⋅110+3+(64−(3⋅1100+62))23⋅1100+62+(7−(5⋅110+8))25⋅110+8+(6−(63⋅1100+7))263⋅1100+7+(−42100+0)21100⋅42+(−46100+0)21100⋅46+(3−(5⋅1100+1))25⋅1100+1+(1−18⋅1100)21100⋅18\begin{aligned}X &= \pm \sqrt{\frac{\left(23 - \left(92 \cdot \frac{1}{100} + 22\right)\right)^{2}}{92 \cdot \frac{1}{100} + 22} + \frac{\left(33 - \left(13 \cdot \frac{1}{100} + 33\right)\right)^{2}}{13 \cdot \frac{1}{100} + 33} + \frac{\left(4 - \left(8 \cdot \frac{1}{100} + 4\right)\right)^{2}}{8 \cdot \frac{1}{100} + 4} + \frac{\left(3 - \left(82 \cdot \frac{1}{100} + 2\right)\right)^{2}}{82 \cdot \frac{1}{100} + 2} + \frac{\left(2 - \left(78 \cdot \frac{1}{100} + 1\right)\right)^{2}}{78 \cdot \frac{1}{100} + 1} + \frac{\left(3 - \left(34 \cdot \frac{1}{100} + 3\right)\right)^{2}}{34 \cdot \frac{1}{100} + 3} + \frac{\left(1 - \left(24 \cdot \frac{1}{100} + 1\right)\right)^{2}}{24 \cdot \frac{1}{100} + 1} + \frac{\left(3 - \left(4 \cdot \frac{1}{10} + 3\right)\right)^{2}}{4 \cdot \frac{1}{10} + 3} + \frac{\left(64 - \left(3 \cdot \frac{1}{100} + 62\right)\right)^{2}}{3 \cdot \frac{1}{100} + 62} + \frac{\left(7 - \left(5 \cdot \frac{1}{10} + 8\right)\right)^{2}}{5 \cdot \frac{1}{10} + 8} + \frac{\left(6 - \left(63 \cdot \frac{1}{100} + 7\right)\right)^{2}}{63 \cdot \frac{1}{100} + 7} + \frac{\left(- \frac{42}{100} + 0\right)^{2}}{\frac{1}{100} \cdot 42} + \frac{\left(- \frac{46}{100} + 0\right)^{2}}{\frac{1}{100} \cdot 46} + \frac{\left(3 - \left(5 \cdot \frac{1}{100} + 1\right)\right)^{2}}{5 \cdot \frac{1}{100} + 1} + \frac{\left(1 - 18 \cdot \frac{1}{100}\right)^{2}}{\frac{1}{100} \cdot 18}} \\ X = \sqrt{\frac{\left(23 - \left(92 \cdot \frac{1}{100} + 22\right)\right)^{2}}{92 \cdot \frac{1}{100} + 22} + \frac{\left(33 - \left(13 \cdot \frac{1}{100} + 33\right)\right)^{2}}{13 \cdot \frac{1}{100} + 33} + \frac{\left(4 - \left(8 \cdot \frac{1}{100} + 4\right)\right)^{2}}{8 \cdot \frac{1}{100} + 4} + \frac{\left(3 - \left(82 \cdot \frac{1}{100} + 2\right)\right)^{2}}{82 \cdot \frac{1}{100} + 2} + \frac{\left(2 - \left(78 \cdot \frac{1}{100} + 1\right)\right)^{2}}{78 \cdot \frac{1}{100} + 1} + \frac{\left(3 - \left(34 \cdot \frac{1}{100} + 3\right)\right)^{2}}{34 \cdot \frac{1}{100} + 3} + \frac{\left(1 - \left(24 \cdot \frac{1}{100} + 1\right)\right)^{2}}{24 \cdot \frac{1}{100} + 1} + \frac{\left(3 - \left(4 \cdot \frac{1}{10} + 3\right)\right)^{2}}{4 \cdot \frac{1}{10} + 3} + \frac{\left(64 - \left(3 \cdot \frac{1}{100} + 62\right)\right)^{2}}{3 \cdot \frac{1}{100} + 62} + \frac{\left(7 - \left(5 \cdot \frac{1}{10} + 8\right)\right)^{2}}{5 \cdot \frac{1}{10} + 8} + \frac{\left(6 - \left(63 \cdot \frac{1}{100} + 7\right)\right)^{2}}{63 \cdot \frac{1}{100} + 7} + \frac{\left(- \frac{42}{100} + 0\right)^{2}}{\frac{1}{100} \cdot 42} + \frac{\left(- \frac{46}{100} + 0\right)^{2}}{\frac{1}{100} \cdot 46} + \frac{\left(3 - \left(5 \cdot \frac{1}{100} + 1\right)\right)^{2}}{5 \cdot \frac{1}{100} + 1} + \frac{\left(1 - 18 \cdot \frac{1}{100}\right)^{2}}{\frac{1}{100} \cdot 18}} &,\, X=-\sqrt{\frac{\left(23 - \left(92 \cdot \frac{1}{100} + 22\right)\right)^{2}}{92 \cdot \frac{1}{100} + 22} + \frac{\left(33 - \left(13 \cdot \frac{1}{100} + 33\right)\right)^{2}}{13 \cdot \frac{1}{100} + 33} + \frac{\left(4 - \left(8 \cdot \frac{1}{100} + 4\right)\right)^{2}}{8 \cdot \frac{1}{100} + 4} + \frac{\left(3 - \left(82 \cdot \frac{1}{100} + 2\right)\right)^{2}}{82 \cdot \frac{1}{100} + 2} + \frac{\left(2 - \left(78 \cdot \frac{1}{100} + 1\right)\right)^{2}}{78 \cdot \frac{1}{100} + 1} + \frac{\left(3 - \left(34 \cdot \frac{1}{100} + 3\right)\right)^{2}}{34 \cdot \frac{1}{100} + 3} + \frac{\left(1 - \left(24 \cdot \frac{1}{100} + 1\right)\right)^{2}}{24 \cdot \frac{1}{100} + 1} + \frac{\left(3 - \left(4 \cdot \frac{1}{10} + 3\right)\right)^{2}}{4 \cdot \frac{1}{10} + 3} + \frac{\left(64 - \left(3 \cdot \frac{1}{100} + 62\right)\right)^{2}}{3 \cdot \frac{1}{100} + 62} + \frac{\left(7 - \left(5 \cdot \frac{1}{10} + 8\right)\right)^{2}}{5 \cdot \frac{1}{10} + 8} + \frac{\left(6 - \left(63 \cdot \frac{1}{100} + 7\right)\right)^{2}}{63 \cdot \frac{1}{100} + 7} + \frac{\left(- \frac{42}{100} + 0\right)^{2}}{\frac{1}{100} \cdot 42} + \frac{\left(- \frac{46}{100} + 0\right)^{2}}{\frac{1}{100} \cdot 46} + \frac{\left(3 - \left(5 \cdot \frac{1}{100} + 1\right)\right)^{2}}{5 \cdot \frac{1}{100} + 1} + \frac{\left(1 - 18 \cdot \frac{1}{100}\right)^{2}}{\frac{1}{100} \cdot 18}}\end{aligned}

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