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Simplifying 128 = 2x(x + -60) Reorder the terms: 128 = 2x(-60 + x) 128 = (-60 * 2x + x * 2x) 128 = (-120x + 2x2) Solving 128 = -120x + 2x2 Solving for variable 'x'. Reorder the terms: 128 + 120x + -2x2 = -120x + 120x + 2x2 + -2x2 Combine like terms: -120x + 120x = 0 128 + 120x + -2x2 = 0 + 2x2 + -2x2 128 + 120x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 128 + 120x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(64 + 60x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(64 + 60x + -1x2)' equal to zero and attempt to solve: Simplifying 64 + 60x + -1x2 = 0 Solving 64 + 60x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -64 + -60x + x2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + -60x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -60x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -60x + x2 = 0 + 64 -60x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -60x + x2 = 64 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = 64 + 900 Reorder the terms: 900 + -60x + x2 = 64 + 900 Combine like terms: 64 + 900 = 964 900 + -60x + x2 = 964 Factor a perfect square on the left side: (x + -30)(x + -30) = 964 Calculate the square root of the right side: 31.048349393 Break this problem into two subproblems by setting (x + -30) equal to 31.048349393 and -31.048349393.Subproblem 1
x + -30 = 31.048349393 Simplifying x + -30 = 31.048349393 Reorder the terms: -30 + x = 31.048349393 Solving -30 + x = 31.048349393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 31.048349393 + 30 Combine like terms: -30 + 30 = 0 0 + x = 31.048349393 + 30 x = 31.048349393 + 30 Combine like terms: 31.048349393 + 30 = 61.048349393 x = 61.048349393 Simplifying x = 61.048349393Subproblem 2
x + -30 = -31.048349393 Simplifying x + -30 = -31.048349393 Reorder the terms: -30 + x = -31.048349393 Solving -30 + x = -31.048349393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -31.048349393 + 30 Combine like terms: -30 + 30 = 0 0 + x = -31.048349393 + 30 x = -31.048349393 + 30 Combine like terms: -31.048349393 + 30 = -1.048349393 x = -1.048349393 Simplifying x = -1.048349393Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.048349393, -1.048349393}Solution
x = {61.048349393, -1.048349393}
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