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Simplifying 2x2 + -32x + -4 = 60 Reorder the terms: -4 + -32x + 2x2 = 60 Solving -4 + -32x + 2x2 = 60 Solving for variable 'x'. Reorder the terms: -4 + -60 + -32x + 2x2 = 60 + -60 Combine like terms: -4 + -60 = -64 -64 + -32x + 2x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -64 + -32x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-32 + -16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-32 + -16x + x2)' equal to zero and attempt to solve: Simplifying -32 + -16x + x2 = 0 Solving -32 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -16x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -16x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -16x + x2 = 0 + 32 -16x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -16x + x2 = 32 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 32 + 64 Reorder the terms: 64 + -16x + x2 = 32 + 64 Combine like terms: 32 + 64 = 96 64 + -16x + x2 = 96 Factor a perfect square on the left side: (x + -8)(x + -8) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (x + -8) equal to 9.797958971 and -9.797958971.Subproblem 1
x + -8 = 9.797958971 Simplifying x + -8 = 9.797958971 Reorder the terms: -8 + x = 9.797958971 Solving -8 + x = 9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 9.797958971 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.797958971 + 8 x = 9.797958971 + 8 Combine like terms: 9.797958971 + 8 = 17.797958971 x = 17.797958971 Simplifying x = 17.797958971Subproblem 2
x + -8 = -9.797958971 Simplifying x + -8 = -9.797958971 Reorder the terms: -8 + x = -9.797958971 Solving -8 + x = -9.797958971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -9.797958971 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.797958971 + 8 x = -9.797958971 + 8 Combine like terms: -9.797958971 + 8 = -1.797958971 x = -1.797958971 Simplifying x = -1.797958971Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.797958971, -1.797958971}Solution
x = {17.797958971, -1.797958971}
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