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Simplifying -16x2 + 128x + 120 = 0 Reorder the terms: 120 + 128x + -16x2 = 0 Solving 120 + 128x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(15 + 16x + -2x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(15 + 16x + -2x2)' equal to zero and attempt to solve: Simplifying 15 + 16x + -2x2 = 0 Solving 15 + 16x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + -8x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -8x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -8x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -8x + x2 = 0 + 7.5 -8x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -8x + x2 = 7.5 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 = 7.5 + 16 Reorder the terms: 16 + -8x + x2 = 7.5 + 16 Combine like terms: 7.5 + 16 = 23.5 16 + -8x + x2 = 23.5 Factor a perfect square on the left side: (x + -4)(x + -4) = 23.5 Calculate the square root of the right side: 4.847679857 Break this problem into two subproblems by setting (x + -4) equal to 4.847679857 and -4.847679857.Subproblem 1
x + -4 = 4.847679857 Simplifying x + -4 = 4.847679857 Reorder the terms: -4 + x = 4.847679857 Solving -4 + x = 4.847679857 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 = 4.847679857 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.847679857 + 4 x = 4.847679857 + 4 Combine like terms: 4.847679857 + 4 = 8.847679857 x = 8.847679857 Simplifying x = 8.847679857Subproblem 2
x + -4 = -4.847679857 Simplifying x + -4 = -4.847679857 Reorder the terms: -4 + x = -4.847679857 Solving -4 + x = -4.847679857 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 = -4.847679857 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.847679857 + 4 x = -4.847679857 + 4 Combine like terms: -4.847679857 + 4 = -0.847679857 x = -0.847679857 Simplifying x = -0.847679857Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.847679857, -0.847679857}Solution
x = {8.847679857, -0.847679857}
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