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Simplifying -16x2 + 128x = -190 Reorder the terms: 128x + -16x2 = -190 Solving 128x + -16x2 = -190 Solving for variable 'x'. Reorder the terms: 190 + 128x + -16x2 = -190 + 190 Combine like terms: -190 + 190 = 0 190 + 128x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(95 + 64x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(95 + 64x + -8x2)' equal to zero and attempt to solve: Simplifying 95 + 64x + -8x2 = 0 Solving 95 + 64x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -11.875 + -8x + x2 = 0 Move the constant term to the right: Add '11.875' to each side of the equation. -11.875 + -8x + 11.875 + x2 = 0 + 11.875 Reorder the terms: -11.875 + 11.875 + -8x + x2 = 0 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + -8x + x2 = 0 + 11.875 -8x + x2 = 0 + 11.875 Combine like terms: 0 + 11.875 = 11.875 -8x + x2 = 11.875 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 = 11.875 + 16 Reorder the terms: 16 + -8x + x2 = 11.875 + 16 Combine like terms: 11.875 + 16 = 27.875 16 + -8x + x2 = 27.875 Factor a perfect square on the left side: (x + -4)(x + -4) = 27.875 Calculate the square root of the right side: 5.27967802 Break this problem into two subproblems by setting (x + -4) equal to 5.27967802 and -5.27967802.Subproblem 1
x + -4 = 5.27967802 Simplifying x + -4 = 5.27967802 Reorder the terms: -4 + x = 5.27967802 Solving -4 + x = 5.27967802 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 = 5.27967802 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.27967802 + 4 x = 5.27967802 + 4 Combine like terms: 5.27967802 + 4 = 9.27967802 x = 9.27967802 Simplifying x = 9.27967802Subproblem 2
x + -4 = -5.27967802 Simplifying x + -4 = -5.27967802 Reorder the terms: -4 + x = -5.27967802 Solving -4 + x = -5.27967802 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 = -5.27967802 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.27967802 + 4 x = -5.27967802 + 4 Combine like terms: -5.27967802 + 4 = -1.27967802 x = -1.27967802 Simplifying x = -1.27967802Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.27967802, -1.27967802}Solution
x = {9.27967802, -1.27967802}
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