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Simplifying x2 + -32x + -256 = 0 Reorder the terms: -256 + -32x + x2 = 0 Solving -256 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '256' to each side of the equation. -256 + -32x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + -32x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + -32x + x2 = 0 + 256 -32x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 -32x + x2 = 256 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = 256 + 256 Reorder the terms: 256 + -32x + x2 = 256 + 256 Combine like terms: 256 + 256 = 512 256 + -32x + x2 = 512 Factor a perfect square on the left side: (x + -16)(x + -16) = 512 Calculate the square root of the right side: 22.627416998 Break this problem into two subproblems by setting (x + -16) equal to 22.627416998 and -22.627416998.Subproblem 1
x + -16 = 22.627416998 Simplifying x + -16 = 22.627416998 Reorder the terms: -16 + x = 22.627416998 Solving -16 + x = 22.627416998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 22.627416998 + 16 Combine like terms: -16 + 16 = 0 0 + x = 22.627416998 + 16 x = 22.627416998 + 16 Combine like terms: 22.627416998 + 16 = 38.627416998 x = 38.627416998 Simplifying x = 38.627416998Subproblem 2
x + -16 = -22.627416998 Simplifying x + -16 = -22.627416998 Reorder the terms: -16 + x = -22.627416998 Solving -16 + x = -22.627416998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -22.627416998 + 16 Combine like terms: -16 + 16 = 0 0 + x = -22.627416998 + 16 x = -22.627416998 + 16 Combine like terms: -22.627416998 + 16 = -6.627416998 x = -6.627416998 Simplifying x = -6.627416998Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.627416998, -6.627416998}
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