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 \({X}^{2} = \frac{{\left( 3 - 1.05 \right)}^{2}}{1.05} + \frac{{\left( 7 - 8.50 \right)}^{2}}{8.50} + \frac{{\left( 0 - 0.46 \right)}^{2}}{0.46} + \frac{{\left( 6 - 7.63 \right)}^{2}}{7.63} + \frac{{\left( 64 - 62.03 \right)}^{2}}{62.03} + \frac{{\left( 3 - 3.34 \right)}^{2}}{3.34} + \frac{{\left( 4 - 4.08 \right)}^{2}}{4.08} + \frac{{\left( 33 - 33.13 \right)}^{2}}{33.13} + \frac{{\left( 2 - 1.78 \right)}^{2}}{1.78} + \frac{{\left( 0 - 0.42 \right)}^{2}}{0.42} + \frac{{\left( 3 - 3.40 \right)}^{2}}{3.40} + \frac{{\left( 1 - 0.18 \right)}^{2}}{0.18} + \frac{{\left( 3 - 2.82 \right)}^{2}}{2.82} + \frac{{\left( 23 - 22.92 \right)}^{2}}{22.92} + \frac{{\left( 1 - 1.24 \right)}^{2}}{1.24}\) for the variable \(X\).

MathBot Answer:

\[\begin{aligned}X &= \frac{\sqrt{34379591626828831104466111746485108996622398}}{1945666523041161570510} \approx 3.0135746\\X &= - \frac{\sqrt{34379591626828831104466111746485108996622398}}{1945666523041161570510} \approx -3.0135746\end{aligned}\]

Take the square root of both sides of the equation $$\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. $$\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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