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Simplifying -16x2 + 128x + -2 = 0 Reorder the terms: -2 + 128x + -16x2 = 0 Solving -2 + 128x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 64x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 64x + -8x2)' equal to zero and attempt to solve: Simplifying -1 + 64x + -8x2 = 0 Solving -1 + 64x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.125 + -8x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -8x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -8x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -8x + x2 = 0 + -0.125 -8x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -8x + x2 = -0.125 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 = -0.125 + 16 Reorder the terms: 16 + -8x + x2 = -0.125 + 16 Combine like terms: -0.125 + 16 = 15.875 16 + -8x + x2 = 15.875 Factor a perfect square on the left side: (x + -4)(x + -4) = 15.875 Calculate the square root of the right side: 3.984344363 Break this problem into two subproblems by setting (x + -4) equal to 3.984344363 and -3.984344363.Subproblem 1
x + -4 = 3.984344363 Simplifying x + -4 = 3.984344363 Reorder the terms: -4 + x = 3.984344363 Solving -4 + x = 3.984344363 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 = 3.984344363 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.984344363 + 4 x = 3.984344363 + 4 Combine like terms: 3.984344363 + 4 = 7.984344363 x = 7.984344363 Simplifying x = 7.984344363Subproblem 2
x + -4 = -3.984344363 Simplifying x + -4 = -3.984344363 Reorder the terms: -4 + x = -3.984344363 Solving -4 + x = -3.984344363 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 = -3.984344363 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.984344363 + 4 x = -3.984344363 + 4 Combine like terms: -3.984344363 + 4 = 0.015655637 x = 0.015655637 Simplifying x = 0.015655637Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.984344363, 0.015655637}Solution
x = {7.984344363, 0.015655637}
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