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Simplifying x2 + x = 135 Reorder the terms: x + x2 = 135 Solving x + x2 = 135 Solving for variable 'x'. Reorder the terms: -135 + x + x2 = 135 + -135 Combine like terms: 135 + -135 = 0 -135 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '135' to each side of the equation. -135 + x + 135 + x2 = 0 + 135 Reorder the terms: -135 + 135 + x + x2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + x + x2 = 0 + 135 x + x2 = 0 + 135 Combine like terms: 0 + 135 = 135 x + x2 = 135 The x term is x. 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. x + 0.25 + x2 = 135 + 0.25 Reorder the terms: 0.25 + x + x2 = 135 + 0.25 Combine like terms: 135 + 0.25 = 135.25 0.25 + x + 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 = 11.12970335 x = 11.12970335 Simplifying x = 11.12970335Subproblem 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 = -12.12970335 x = -12.12970335 Simplifying x = -12.12970335Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.12970335, -12.12970335}
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