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Simplifying 36x4 + 1132x2 + -432 = 0 Reorder the terms: -432 + 1132x2 + 36x4 = 0 Solving -432 + 1132x2 + 36x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-108 + 283x2 + 9x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-108 + 283x2 + 9x4)' equal to zero and attempt to solve: Simplifying -108 + 283x2 + 9x4 = 0 Solving -108 + 283x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -12 + 31.44444444x2 + x4 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + 31.44444444x2 + 12 + x4 = 0 + 12 Reorder the terms: -12 + 12 + 31.44444444x2 + x4 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 31.44444444x2 + x4 = 0 + 12 31.44444444x2 + x4 = 0 + 12 Combine like terms: 0 + 12 = 12 31.44444444x2 + x4 = 12 The x term is 31.44444444x2. Take half its coefficient (15.72222222). Square it (247.1882715) and add it to both sides. Add '247.1882715' to each side of the equation. 31.44444444x2 + 247.1882715 + x4 = 12 + 247.1882715 Reorder the terms: 247.1882715 + 31.44444444x2 + x4 = 12 + 247.1882715 Combine like terms: 12 + 247.1882715 = 259.1882715 247.1882715 + 31.44444444x2 + x4 = 259.1882715 Factor a perfect square on the left side: (x2 + 15.72222222)(x2 + 15.72222222) = 259.1882715 Calculate the square root of the right side: 16.099325188 Break this problem into two subproblems by setting (x2 + 15.72222222) equal to 16.099325188 and -16.099325188.Subproblem 1
x2 + 15.72222222 = 16.099325188 Simplifying x2 + 15.72222222 = 16.099325188 Reorder the terms: 15.72222222 + x2 = 16.099325188 Solving 15.72222222 + x2 = 16.099325188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.72222222' to each side of the equation. 15.72222222 + -15.72222222 + x2 = 16.099325188 + -15.72222222 Combine like terms: 15.72222222 + -15.72222222 = 0.00000000 0.00000000 + x2 = 16.099325188 + -15.72222222 x2 = 16.099325188 + -15.72222222 Combine like terms: 16.099325188 + -15.72222222 = 0.377102968 x2 = 0.377102968 Simplifying x2 = 0.377102968 Take the square root of each side: x = {-0.614087101, 0.614087101}Subproblem 2
x2 + 15.72222222 = -16.099325188 Simplifying x2 + 15.72222222 = -16.099325188 Reorder the terms: 15.72222222 + x2 = -16.099325188 Solving 15.72222222 + x2 = -16.099325188 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.72222222' to each side of the equation. 15.72222222 + -15.72222222 + x2 = -16.099325188 + -15.72222222 Combine like terms: 15.72222222 + -15.72222222 = 0.00000000 0.00000000 + x2 = -16.099325188 + -15.72222222 x2 = -16.099325188 + -15.72222222 Combine like terms: -16.099325188 + -15.72222222 = -31.821547408 x2 = -31.821547408 Simplifying x2 = -31.821547408 Reorder the terms: 31.821547408 + x2 = -31.821547408 + 31.821547408 Combine like terms: -31.821547408 + 31.821547408 = 0.000000000 31.821547408 + 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. 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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