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Simplifying 8(x2 + -2x + -32) = 0 Reorder the terms: 8(-32 + -2x + x2) = 0 (-32 * 8 + -2x * 8 + x2 * 8) = 0 (-256 + -16x + 8x2) = 0 Solving -256 + -16x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-32 + -2x + x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-32 + -2x + x2)' equal to zero and attempt to solve: Simplifying -32 + -2x + x2 = 0 Solving -32 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -2x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -2x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -2x + x2 = 0 + 32 -2x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -2x + x2 = 32 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 32 + 1 Reorder the terms: 1 + -2x + x2 = 32 + 1 Combine like terms: 32 + 1 = 33 1 + -2x + x2 = 33 Factor a perfect square on the left side: (x + -1)(x + -1) = 33 Calculate the square root of the right side: 5.744562647 Break this problem into two subproblems by setting (x + -1) equal to 5.744562647 and -5.744562647.Subproblem 1
x + -1 = 5.744562647 Simplifying x + -1 = 5.744562647 Reorder the terms: -1 + x = 5.744562647 Solving -1 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.744562647 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.744562647 + 1 x = 5.744562647 + 1 Combine like terms: 5.744562647 + 1 = 6.744562647 x = 6.744562647 Simplifying x = 6.744562647Subproblem 2
x + -1 = -5.744562647 Simplifying x + -1 = -5.744562647 Reorder the terms: -1 + x = -5.744562647 Solving -1 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.744562647 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.744562647 + 1 x = -5.744562647 + 1 Combine like terms: -5.744562647 + 1 = -4.744562647 x = -4.744562647 Simplifying x = -4.744562647Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.744562647, -4.744562647}Solution
x = {6.744562647, -4.744562647}
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