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Simplifying x2 + -1x + -135 = 0 Reorder the terms: -135 + -1x + x2 = 0 Solving -135 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '135' to each side of the equation. -135 + -1x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + -1x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + -1x + x2 = 0 + 135 -1x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 -1x + x2 = 135 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 = 135 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 135 + 0.25 Combine like terms: 135 + 0.25 = 135.25 0.25 + -1x + x2 = 135.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 135.25 Calculate the square root of the right side: 11.62970335 Break this problem into two subproblems by setting (x + -0.5) equal to 11.62970335 and -11.62970335.Subproblem 1
x + -0.5 = 11.62970335 Simplifying x + -0.5 = 11.62970335 Reorder the terms: -0.5 + x = 11.62970335 Solving -0.5 + x = 11.62970335 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 = 11.62970335 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 11.62970335 + 0.5 x = 11.62970335 + 0.5 Combine like terms: 11.62970335 + 0.5 = 12.12970335 x = 12.12970335 Simplifying x = 12.12970335Subproblem 2
x + -0.5 = -11.62970335 Simplifying x + -0.5 = -11.62970335 Reorder the terms: -0.5 + x = -11.62970335 Solving -0.5 + x = -11.62970335 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 = -11.62970335 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -11.62970335 + 0.5 x = -11.62970335 + 0.5 Combine like terms: -11.62970335 + 0.5 = -11.12970335 x = -11.12970335 Simplifying x = -11.12970335Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.12970335, -11.12970335}
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