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Simplifying 4x2 + -32x + 58 = 0 Reorder the terms: 58 + -32x + 4x2 = 0 Solving 58 + -32x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(29 + -16x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(29 + -16x + 2x2)' equal to zero and attempt to solve: Simplifying 29 + -16x + 2x2 = 0 Solving 29 + -16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14.5 + -8x + x2 = 0 Move the constant term to the right: Add '-14.5' to each side of the equation. 14.5 + -8x + -14.5 + x2 = 0 + -14.5 Reorder the terms: 14.5 + -14.5 + -8x + x2 = 0 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + -8x + x2 = 0 + -14.5 -8x + x2 = 0 + -14.5 Combine like terms: 0 + -14.5 = -14.5 -8x + x2 = -14.5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -14.5 + 16 Reorder the terms: 16 + -8x + x2 = -14.5 + 16 Combine like terms: -14.5 + 16 = 1.5 16 + -8x + x2 = 1.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (x + -4) equal to 1.224744871 and -1.224744871.Subproblem 1
x + -4 = 1.224744871 Simplifying x + -4 = 1.224744871 Reorder the terms: -4 + x = 1.224744871 Solving -4 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 1.224744871 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.224744871 + 4 x = 1.224744871 + 4 Combine like terms: 1.224744871 + 4 = 5.224744871 x = 5.224744871 Simplifying x = 5.224744871Subproblem 2
x + -4 = -1.224744871 Simplifying x + -4 = -1.224744871 Reorder the terms: -4 + x = -1.224744871 Solving -4 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -1.224744871 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.224744871 + 4 x = -1.224744871 + 4 Combine like terms: -1.224744871 + 4 = 2.775255129 x = 2.775255129 Simplifying x = 2.775255129Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.224744871, 2.775255129}Solution
x = {5.224744871, 2.775255129}
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