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Simplifying 0 = -16x2 + 64x + 2 Reorder the terms: 0 = 2 + 64x + -16x2 Solving 0 = 2 + 64x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -64x + 16x2 = 2 + 64x + -16x2 + -2 + -64x + 16x2 Reorder the terms: -2 + -64x + 16x2 = 2 + -2 + 64x + -64x + -16x2 + 16x2 Combine like terms: 2 + -2 = 0 -2 + -64x + 16x2 = 0 + 64x + -64x + -16x2 + 16x2 -2 + -64x + 16x2 = 64x + -64x + -16x2 + 16x2 Combine like terms: 64x + -64x = 0 -2 + -64x + 16x2 = 0 + -16x2 + 16x2 -2 + -64x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -2 + -64x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -32x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -32x + 8x2)' equal to zero and attempt to solve: Simplifying -1 + -32x + 8x2 = 0 Solving -1 + -32x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -4x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -4x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -4x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -4x + x2 = 0 + 0.125 -4x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -4x + x2 = 0.125 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 0.125 + 4 Reorder the terms: 4 + -4x + x2 = 0.125 + 4 Combine like terms: 0.125 + 4 = 4.125 4 + -4x + x2 = 4.125 Factor a perfect square on the left side: (x + -2)(x + -2) = 4.125 Calculate the square root of the right side: 2.031009601 Break this problem into two subproblems by setting (x + -2) equal to 2.031009601 and -2.031009601.Subproblem 1
x + -2 = 2.031009601 Simplifying x + -2 = 2.031009601 Reorder the terms: -2 + x = 2.031009601 Solving -2 + x = 2.031009601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.031009601 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.031009601 + 2 x = 2.031009601 + 2 Combine like terms: 2.031009601 + 2 = 4.031009601 x = 4.031009601 Simplifying x = 4.031009601Subproblem 2
x + -2 = -2.031009601 Simplifying x + -2 = -2.031009601 Reorder the terms: -2 + x = -2.031009601 Solving -2 + x = -2.031009601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.031009601 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.031009601 + 2 x = -2.031009601 + 2 Combine like terms: -2.031009601 + 2 = -0.031009601 x = -0.031009601 Simplifying x = -0.031009601Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.031009601, -0.031009601}Solution
x = {4.031009601, -0.031009601}
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