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Simplifying -16x2 + 128x = 92 Reorder the terms: 128x + -16x2 = 92 Solving 128x + -16x2 = 92 Solving for variable 'x'. Reorder the terms: -92 + 128x + -16x2 = 92 + -92 Combine like terms: 92 + -92 = 0 -92 + 128x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-23 + 32x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-23 + 32x + -4x2)' equal to zero and attempt to solve: Simplifying -23 + 32x + -4x2 = 0 Solving -23 + 32x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 5.75 + -8x + x2 = 0 Move the constant term to the right: Add '-5.75' to each side of the equation. 5.75 + -8x + -5.75 + x2 = 0 + -5.75 Reorder the terms: 5.75 + -5.75 + -8x + x2 = 0 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + -8x + x2 = 0 + -5.75 -8x + x2 = 0 + -5.75 Combine like terms: 0 + -5.75 = -5.75 -8x + x2 = -5.75 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 = -5.75 + 16 Reorder the terms: 16 + -8x + x2 = -5.75 + 16 Combine like terms: -5.75 + 16 = 10.25 16 + -8x + x2 = 10.25 Factor a perfect square on the left side: (x + -4)(x + -4) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -4) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -4 = 3.201562119 Simplifying x + -4 = 3.201562119 Reorder the terms: -4 + x = 3.201562119 Solving -4 + x = 3.201562119 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 = 3.201562119 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.201562119 + 4 x = 3.201562119 + 4 Combine like terms: 3.201562119 + 4 = 7.201562119 x = 7.201562119 Simplifying x = 7.201562119Subproblem 2
x + -4 = -3.201562119 Simplifying x + -4 = -3.201562119 Reorder the terms: -4 + x = -3.201562119 Solving -4 + x = -3.201562119 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 = -3.201562119 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.201562119 + 4 x = -3.201562119 + 4 Combine like terms: -3.201562119 + 4 = 0.798437881 x = 0.798437881 Simplifying x = 0.798437881Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.201562119, 0.798437881}Solution
x = {7.201562119, 0.798437881}
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