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Simplifying x2 + -1x + -136 = 0 Reorder the terms: -136 + -1x + x2 = 0 Solving -136 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '136' to each side of the equation. -136 + -1x + 136 + x2 = 0 + 136 Reorder the terms: -136 + 136 + -1x + x2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + -1x + x2 = 0 + 136 -1x + x2 = 0 + 136 Combine like terms: 0 + 136 = 136 -1x + x2 = 136 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 = 136 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 136 + 0.25 Combine like terms: 136 + 0.25 = 136.25 0.25 + -1x + x2 = 136.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 136.25 Calculate the square root of the right side: 11.67261753 Break this problem into two subproblems by setting (x + -0.5) equal to 11.67261753 and -11.67261753.Subproblem 1
x + -0.5 = 11.67261753 Simplifying x + -0.5 = 11.67261753 Reorder the terms: -0.5 + x = 11.67261753 Solving -0.5 + x = 11.67261753 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 = 11.67261753 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 11.67261753 + 0.5 x = 11.67261753 + 0.5 Combine like terms: 11.67261753 + 0.5 = 12.17261753 x = 12.17261753 Simplifying x = 12.17261753Subproblem 2
x + -0.5 = -11.67261753 Simplifying x + -0.5 = -11.67261753 Reorder the terms: -0.5 + x = -11.67261753 Solving -0.5 + x = -11.67261753 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 = -11.67261753 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -11.67261753 + 0.5 x = -11.67261753 + 0.5 Combine like terms: -11.67261753 + 0.5 = -11.17261753 x = -11.17261753 Simplifying x = -11.17261753Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.17261753, -11.17261753}
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