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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 = 16.125 16 + -8x + x2 = 16.125 Factor a perfect square on the left side: (x + -4)(x + -4) = 16.125 Calculate the square root of the right side: 4.015594601 Break this problem into two subproblems by setting (x + -4) equal to 4.015594601 and -4.015594601.Subproblem 1
x + -4 = 4.015594601 Simplifying x + -4 = 4.015594601 Reorder the terms: -4 + x = 4.015594601 Solving -4 + x = 4.015594601 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 = 4.015594601 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.015594601 + 4 x = 4.015594601 + 4 Combine like terms: 4.015594601 + 4 = 8.015594601 x = 8.015594601 Simplifying x = 8.015594601Subproblem 2
x + -4 = -4.015594601 Simplifying x + -4 = -4.015594601 Reorder the terms: -4 + x = -4.015594601 Solving -4 + x = -4.015594601 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 = -4.015594601 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.015594601 + 4 x = -4.015594601 + 4 Combine like terms: -4.015594601 + 4 = -0.015594601 x = -0.015594601 Simplifying x = -0.015594601Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.015594601, -0.015594601}Solution
x = {8.015594601, -0.015594601}
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