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Simplifying 35x4 + 16x2 + -8 = 0 Reorder the terms: -8 + 16x2 + 35x4 = 0 Solving -8 + 16x2 + 35x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -0.2285714286 + 0.4571428571x2 + x4 = 0 Move the constant term to the right: Add '0.2285714286' to each side of the equation. -0.2285714286 + 0.4571428571x2 + 0.2285714286 + x4 = 0 + 0.2285714286 Reorder the terms: -0.2285714286 + 0.2285714286 + 0.4571428571x2 + x4 = 0 + 0.2285714286 Combine like terms: -0.2285714286 + 0.2285714286 = 0.0000000000 0.0000000000 + 0.4571428571x2 + x4 = 0 + 0.2285714286 0.4571428571x2 + x4 = 0 + 0.2285714286 Combine like terms: 0 + 0.2285714286 = 0.2285714286 0.4571428571x2 + x4 = 0.2285714286 The x term is 0.4571428571x2. Take half its coefficient (0.2285714286). Square it (0.05224489797) and add it to both sides. Add '0.05224489797' to each side of the equation. 0.4571428571x2 + 0.05224489797 + x4 = 0.2285714286 + 0.05224489797 Reorder the terms: 0.05224489797 + 0.4571428571x2 + x4 = 0.2285714286 + 0.05224489797 Combine like terms: 0.2285714286 + 0.05224489797 = 0.28081632657 0.05224489797 + 0.4571428571x2 + x4 = 0.28081632657 Factor a perfect square on the left side: (x2 + 0.2285714286)(x2 + 0.2285714286) = 0.28081632657 Calculate the square root of the right side: 0.529921057 Break this problem into two subproblems by setting (x2 + 0.2285714286) equal to 0.529921057 and -0.529921057.Subproblem 1
x2 + 0.2285714286 = 0.529921057 Simplifying x2 + 0.2285714286 = 0.529921057 Reorder the terms: 0.2285714286 + x2 = 0.529921057 Solving 0.2285714286 + x2 = 0.529921057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2285714286' to each side of the equation. 0.2285714286 + -0.2285714286 + x2 = 0.529921057 + -0.2285714286 Combine like terms: 0.2285714286 + -0.2285714286 = 0.0000000000 0.0000000000 + x2 = 0.529921057 + -0.2285714286 x2 = 0.529921057 + -0.2285714286 Combine like terms: 0.529921057 + -0.2285714286 = 0.3013496284 x2 = 0.3013496284 Simplifying x2 = 0.3013496284 Take the square root of each side: x = {-0.548953211, 0.548953211}Subproblem 2
x2 + 0.2285714286 = -0.529921057 Simplifying x2 + 0.2285714286 = -0.529921057 Reorder the terms: 0.2285714286 + x2 = -0.529921057 Solving 0.2285714286 + x2 = -0.529921057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2285714286' to each side of the equation. 0.2285714286 + -0.2285714286 + x2 = -0.529921057 + -0.2285714286 Combine like terms: 0.2285714286 + -0.2285714286 = 0.0000000000 0.0000000000 + x2 = -0.529921057 + -0.2285714286 x2 = -0.529921057 + -0.2285714286 Combine like terms: -0.529921057 + -0.2285714286 = -0.7584924856 x2 = -0.7584924856 Simplifying x2 = -0.7584924856 Reorder the terms: 0.7584924856 + x2 = -0.7584924856 + 0.7584924856 Combine like terms: -0.7584924856 + 0.7584924856 = 0.0000000000 0.7584924856 + x2 = 0.0000000000 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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