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Simplifying x2 + x = 138 Reorder the terms: x + x2 = 138 Solving x + x2 = 138 Solving for variable 'x'. Reorder the terms: -138 + x + x2 = 138 + -138 Combine like terms: 138 + -138 = 0 -138 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '138' to each side of the equation. -138 + x + 138 + x2 = 0 + 138 Reorder the terms: -138 + 138 + x + x2 = 0 + 138 Combine like terms: -138 + 138 = 0 0 + x + x2 = 0 + 138 x + x2 = 0 + 138 Combine like terms: 0 + 138 = 138 x + x2 = 138 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 = 138 + 0.25 Reorder the terms: 0.25 + x + x2 = 138 + 0.25 Combine like terms: 138 + 0.25 = 138.25 0.25 + x + x2 = 138.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 138.25 Calculate the square root of the right side: 11.757976016 Break this problem into two subproblems by setting (x + 0.5) equal to 11.757976016 and -11.757976016.Subproblem 1
x + 0.5 = 11.757976016 Simplifying x + 0.5 = 11.757976016 Reorder the terms: 0.5 + x = 11.757976016 Solving 0.5 + x = 11.757976016 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 = 11.757976016 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.757976016 + -0.5 x = 11.757976016 + -0.5 Combine like terms: 11.757976016 + -0.5 = 11.257976016 x = 11.257976016 Simplifying x = 11.257976016Subproblem 2
x + 0.5 = -11.757976016 Simplifying x + 0.5 = -11.757976016 Reorder the terms: 0.5 + x = -11.757976016 Solving 0.5 + x = -11.757976016 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 = -11.757976016 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.757976016 + -0.5 x = -11.757976016 + -0.5 Combine like terms: -11.757976016 + -0.5 = -12.257976016 x = -12.257976016 Simplifying x = -12.257976016Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.257976016, -12.257976016}
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