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Simplifying -16x2 + 128x + 4096 = 0 Reorder the terms: 4096 + 128x + -16x2 = 0 Solving 4096 + 128x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(256 + 8x + -1x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(256 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying 256 + 8x + -1x2 = 0 Solving 256 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -256 + -8x + x2 = 0 Move the constant term to the right: Add '256' to each side of the equation. -256 + -8x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + -8x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + -8x + x2 = 0 + 256 -8x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 -8x + x2 = 256 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 = 256 + 16 Reorder the terms: 16 + -8x + x2 = 256 + 16 Combine like terms: 256 + 16 = 272 16 + -8x + x2 = 272 Factor a perfect square on the left side: (x + -4)(x + -4) = 272 Calculate the square root of the right side: 16.492422502 Break this problem into two subproblems by setting (x + -4) equal to 16.492422502 and -16.492422502.Subproblem 1
x + -4 = 16.492422502 Simplifying x + -4 = 16.492422502 Reorder the terms: -4 + x = 16.492422502 Solving -4 + x = 16.492422502 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 = 16.492422502 + 4 Combine like terms: -4 + 4 = 0 0 + x = 16.492422502 + 4 x = 16.492422502 + 4 Combine like terms: 16.492422502 + 4 = 20.492422502 x = 20.492422502 Simplifying x = 20.492422502Subproblem 2
x + -4 = -16.492422502 Simplifying x + -4 = -16.492422502 Reorder the terms: -4 + x = -16.492422502 Solving -4 + x = -16.492422502 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 = -16.492422502 + 4 Combine like terms: -4 + 4 = 0 0 + x = -16.492422502 + 4 x = -16.492422502 + 4 Combine like terms: -16.492422502 + 4 = -12.492422502 x = -12.492422502 Simplifying x = -12.492422502Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.492422502, -12.492422502}Solution
x = {20.492422502, -12.492422502}
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