0.03x^4 - 0.8x^3 + 6x^2 - 5 = 0
asked by guest
You asked:
Solve the equation
0.03 x 4 − 0.8 x 3 + 6 x 2 − 5 = 0 0.03 {x}^{4} - 0.8 {x}^{3} + 6 {x}^{2} - 5 = 0 0.03 x 4 − 0.8 x 3 + 6 x 2 − 5 = 0 for the variable
x x x .
MathBot Answer:
The 4 solutions to the equation are:
x = 20 3 − 400 9 + 2 950000 27 + 95000 5 27 3 + 19000 9 950000 27 + 95000 5 27 3 2 − 800 9 − 2 950000 27 + 95000 5 27 3 − 19000 9 950000 27 + 95000 5 27 3 + 16000 27 400 9 + 2 950000 27 + 95000 5 27 3 + 19000 9 950000 27 + 95000 5 27 3 2 ≈ − 0.86304558 x = 20 3 + 800 9 − 2 950000 27 + 95000 5 27 3 − 19000 9 950000 27 + 95000 5 27 3 + 16000 27 400 9 + 2 950000 27 + 95000 5 27 3 + 19000 9 950000 27 + 95000 5 27 3 2 − 400 9 + 2 950000 27 + 95000 5 27 3 + 19000 9 950000 27 + 95000 5 27 3 2 ≈ 0.97611463 x = 400 9 + 19000 9 95000 5 27 + 950000 27 3 + 2 95000 5 27 + 950000 27 3 2 + 20 3 − i − 800 9 + 16000 27 400 9 + 19000 9 95000 5 27 + 950000 27 3 + 2 95000 5 27 + 950000 27 3 + 19000 9 95000 5 27 + 950000 27 3 + 2 95000 5 27 + 950000 27 3 2 ≈ 13.276799 − 4.6439913 i x = 400 9 + 19000 9 95000 5 27 + 950000 27 3 + 2 95000 5 27 + 950000 27 3 2 + 20 3 + i − 800 9 + 16000 27 400 9 + 19000 9 95000 5 27 + 950000 27 3 + 2 95000 5 27 + 950000 27 3 + 19000 9 95000 5 27 + 950000 27 3 + 2 95000 5 27 + 950000 27 3 2 ≈ 13.276799 + 4.6439913 i \begin{aligned}x &= \frac{20}{3} - \frac{\sqrt{\frac{400}{9} + 2 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}} + \frac{19000}{9 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}}}}}{2} - \frac{\sqrt{\frac{800}{9} - 2 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}} - \frac{19000}{9 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}}} + \frac{16000}{27 \sqrt{\frac{400}{9} + 2 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}} + \frac{19000}{9 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}}}}}}}{2} \approx -0.86304558\\x &= \frac{20}{3} + \frac{\sqrt{\frac{800}{9} - 2 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}} - \frac{19000}{9 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}}} + \frac{16000}{27 \sqrt{\frac{400}{9} + 2 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}} + \frac{19000}{9 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}}}}}}}{2} - \frac{\sqrt{\frac{400}{9} + 2 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}} + \frac{19000}{9 \sqrt[3]{\frac{950000}{27} + \frac{95000 \sqrt{5}}{27}}}}}{2} \approx 0.97611463\\x &= \frac{\sqrt{\frac{400}{9} + \frac{19000}{9 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}} + 2 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}}}{2} + \frac{20}{3} - \frac{i \sqrt{- \frac{800}{9} + \frac{16000}{27 \sqrt{\frac{400}{9} + \frac{19000}{9 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}} + 2 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}}} + \frac{19000}{9 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}} + 2 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}}}{2} \approx 13.276799 -4.6439913 i\\x &= \frac{\sqrt{\frac{400}{9} + \frac{19000}{9 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}} + 2 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}}}{2} + \frac{20}{3} + \frac{i \sqrt{- \frac{800}{9} + \frac{16000}{27 \sqrt{\frac{400}{9} + \frac{19000}{9 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}} + 2 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}}} + \frac{19000}{9 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}} + 2 \sqrt[3]{\frac{95000 \sqrt{5}}{27} + \frac{950000}{27}}}}{2} \approx 13.276799 + 4.6439913 i\end{aligned} x x x x = 3 20 − 2 9 400 + 2 3 27 950000 + 27 95000 5 + 9 3 27 950000 + 27 95000 5 19000 − 2 9 800 − 2 3 27 950000 + 27 95000 5 − 9 3 27 950000 + 27 95000 5 19000 + 27 9 400 + 2 3 27 950000 + 27 95000 5 + 9 3 27 950000 + 27 95000 5 19000 16000 ≈ − 0.86304558 = 3 20 + 2 9 800 − 2 3 27 950000 + 27 95000 5 − 9 3 27 950000 + 27 95000 5 19000 + 27 9 400 + 2 3 27 950000 + 27 95000 5 + 9 3 27 950000 + 27 95000 5 19000 16000 − 2 9 400 + 2 3 27 950000 + 27 95000 5 + 9 3 27 950000 + 27 95000 5 19000 ≈ 0.97611463 = 2 9 400 + 9 3 27 95000 5 + 27 950000 19000 + 2 3 27 95000 5 + 27 950000 + 3 20 − 2 i − 9 800 + 27 9 400 + 9 3 27 95000 5 + 27 950000 19000 + 2 3 27 95000 5 + 27 950000 16000 + 9 3 27 95000 5 + 27 950000 19000 + 2 3 27 95000 5 + 27 950000 ≈ 13.276799 − 4.6439913 i = 2 9 400 + 9 3 27 95000 5 + 27 950000 19000 + 2 3 27 95000 5 + 27 950000 + 3 20 + 2 i − 9 800 + 27 9 400 + 9 3 27 95000 5 + 27 950000 19000 + 2 3 27 95000 5 + 27 950000 16000 + 9 3 27 95000 5 + 27 950000 19000 + 2 3 27 95000 5 + 27 950000 ≈ 13.276799 + 4.6439913 i
i i i imaginary unit , defined as i 2 = − 1 i^2 = -1 i 2 = − 1
