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Simplifying 2x2 + 32x = 512 Reorder the terms: 32x + 2x2 = 512 Solving 32x + 2x2 = 512 Solving for variable 'x'. Reorder the terms: -512 + 32x + 2x2 = 512 + -512 Combine like terms: 512 + -512 = 0 -512 + 32x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-256 + 16x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-256 + 16x + x2)' equal to zero and attempt to solve: Simplifying -256 + 16x + x2 = 0 Solving -256 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + 16x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 16x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 16x + x2 = 0 + 256 16x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 16x + x2 = 256 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 256 + 64 Reorder the terms: 64 + 16x + x2 = 256 + 64 Combine like terms: 256 + 64 = 320 64 + 16x + x2 = 320 Factor a perfect square on the left side: (x + 8)(x + 8) = 320 Calculate the square root of the right side: 17.88854382 Break this problem into two subproblems by setting (x + 8) equal to 17.88854382 and -17.88854382.Subproblem 1
x + 8 = 17.88854382 Simplifying x + 8 = 17.88854382 Reorder the terms: 8 + x = 17.88854382 Solving 8 + x = 17.88854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 17.88854382 + -8 Combine like terms: 8 + -8 = 0 0 + x = 17.88854382 + -8 x = 17.88854382 + -8 Combine like terms: 17.88854382 + -8 = 9.88854382 x = 9.88854382 Simplifying x = 9.88854382Subproblem 2
x + 8 = -17.88854382 Simplifying x + 8 = -17.88854382 Reorder the terms: 8 + x = -17.88854382 Solving 8 + x = -17.88854382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -17.88854382 + -8 Combine like terms: 8 + -8 = 0 0 + x = -17.88854382 + -8 x = -17.88854382 + -8 Combine like terms: -17.88854382 + -8 = -25.88854382 x = -25.88854382 Simplifying x = -25.88854382Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.88854382, -25.88854382}Solution
x = {9.88854382, -25.88854382}
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