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Simplifying -1x(1 + -1x) * 2 = 16 Reorder the terms for easier multiplication: -1 * 2x(1 + -1x) = 16 Multiply -1 * 2 -2x(1 + -1x) = 16 (1 * -2x + -1x * -2x) = 16 (-2x + 2x2) = 16 Solving -2x + 2x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + -2x + 2x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -1x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -1x + x2)' equal to zero and attempt to solve: Simplifying -8 + -1x + x2 = 0 Solving -8 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -1x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -1x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x + x2 = 0 + 8 -1x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -1x + x2 = 8 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 8 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 8 + 0.25 Combine like terms: 8 + 0.25 = 8.25 0.25 + -1x + x2 = 8.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + -0.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + -0.5 = 2.872281323 Simplifying x + -0.5 = 2.872281323 Reorder the terms: -0.5 + x = 2.872281323 Solving -0.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.872281323 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.872281323 + 0.5 x = 2.872281323 + 0.5 Combine like terms: 2.872281323 + 0.5 = 3.372281323 x = 3.372281323 Simplifying x = 3.372281323Subproblem 2
x + -0.5 = -2.872281323 Simplifying x + -0.5 = -2.872281323 Reorder the terms: -0.5 + x = -2.872281323 Solving -0.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.872281323 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.872281323 + 0.5 x = -2.872281323 + 0.5 Combine like terms: -2.872281323 + 0.5 = -2.372281323 x = -2.372281323 Simplifying x = -2.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.372281323, -2.372281323}Solution
x = {3.372281323, -2.372281323}
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