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Simplifying -2x2 + 32x + 120 = 0 Reorder the terms: 120 + 32x + -2x2 = 0 Solving 120 + 32x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(60 + 16x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + 16x + -1x2)' equal to zero and attempt to solve: Simplifying 60 + 16x + -1x2 = 0 Solving 60 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -60 + -16x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -16x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -16x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -16x + x2 = 0 + 60 -16x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -16x + x2 = 60 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 = 60 + 64 Reorder the terms: 64 + -16x + x2 = 60 + 64 Combine like terms: 60 + 64 = 124 64 + -16x + x2 = 124 Factor a perfect square on the left side: (x + -8)(x + -8) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (x + -8) equal to 11.135528726 and -11.135528726.Subproblem 1
x + -8 = 11.135528726 Simplifying x + -8 = 11.135528726 Reorder the terms: -8 + x = 11.135528726 Solving -8 + x = 11.135528726 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 = 11.135528726 + 8 Combine like terms: -8 + 8 = 0 0 + x = 11.135528726 + 8 x = 11.135528726 + 8 Combine like terms: 11.135528726 + 8 = 19.135528726 x = 19.135528726 Simplifying x = 19.135528726Subproblem 2
x + -8 = -11.135528726 Simplifying x + -8 = -11.135528726 Reorder the terms: -8 + x = -11.135528726 Solving -8 + x = -11.135528726 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 = -11.135528726 + 8 Combine like terms: -8 + 8 = 0 0 + x = -11.135528726 + 8 x = -11.135528726 + 8 Combine like terms: -11.135528726 + 8 = -3.135528726 x = -3.135528726 Simplifying x = -3.135528726Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.135528726, -3.135528726}Solution
x = {19.135528726, -3.135528726}
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