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Simplifying 2x4 + -255 + 7x2 = 0 Reorder the terms: -255 + 7x2 + 2x4 = 0 Solving -255 + 7x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -127.5 + 3.5x2 + x4 = 0 Move the constant term to the right: Add '127.5' to each side of the equation. -127.5 + 3.5x2 + 127.5 + x4 = 0 + 127.5 Reorder the terms: -127.5 + 127.5 + 3.5x2 + x4 = 0 + 127.5 Combine like terms: -127.5 + 127.5 = 0.0 0.0 + 3.5x2 + x4 = 0 + 127.5 3.5x2 + x4 = 0 + 127.5 Combine like terms: 0 + 127.5 = 127.5 3.5x2 + x4 = 127.5 The x term is 3.5x2. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x2 + 3.0625 + x4 = 127.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x2 + x4 = 127.5 + 3.0625 Combine like terms: 127.5 + 3.0625 = 130.5625 3.0625 + 3.5x2 + x4 = 130.5625 Factor a perfect square on the left side: (x2 + 1.75)(x2 + 1.75) = 130.5625 Calculate the square root of the right side: 11.426394882 Break this problem into two subproblems by setting (x2 + 1.75) equal to 11.426394882 and -11.426394882.Subproblem 1
x2 + 1.75 = 11.426394882 Simplifying x2 + 1.75 = 11.426394882 Reorder the terms: 1.75 + x2 = 11.426394882 Solving 1.75 + x2 = 11.426394882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x2 = 11.426394882 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x2 = 11.426394882 + -1.75 x2 = 11.426394882 + -1.75 Combine like terms: 11.426394882 + -1.75 = 9.676394882 x2 = 9.676394882 Simplifying x2 = 9.676394882 Take the square root of each side: x = {-3.110690419, 3.110690419}Subproblem 2
x2 + 1.75 = -11.426394882 Simplifying x2 + 1.75 = -11.426394882 Reorder the terms: 1.75 + x2 = -11.426394882 Solving 1.75 + x2 = -11.426394882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x2 = -11.426394882 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x2 = -11.426394882 + -1.75 x2 = -11.426394882 + -1.75 Combine like terms: -11.426394882 + -1.75 = -13.176394882 x2 = -13.176394882 Simplifying x2 = -13.176394882 Reorder the terms: 13.176394882 + x2 = -13.176394882 + 13.176394882 Combine like terms: -13.176394882 + 13.176394882 = 0.000000000 13.176394882 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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