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Simplifying x^{2}+ x = 13 Reorder the terms: x + x^{2}= 13 Solving x + x^{2}= 13 Solving for variable 'x'. Reorder the terms: -13 + x + x^{2}= 13 + -13 Combine like terms: 13 + -13 = 0 -13 + x + x^{2}= 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + x + 13 + x^{2}= 0 + 13 Reorder the terms: -13 + 13 + x + x^{2}= 0 + 13 Combine like terms: -13 + 13 = 0 0 + x + x^{2}= 0 + 13 x + x^{2}= 0 + 13 Combine like terms: 0 + 13 = 13 x + x^{2}= 13 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 + x^{2}= 13 + 0.25 Reorder the terms: 0.25 + x + x^{2}= 13 + 0.25 Combine like terms: 13 + 0.25 = 13.25 0.25 + x + x^{2}= 13.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + 0.5) equal to 3.640054945 and -3.640054945.## Subproblem 1

x + 0.5 = 3.640054945 Simplifying x + 0.5 = 3.640054945 Reorder the terms: 0.5 + x = 3.640054945 Solving 0.5 + x = 3.640054945 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 = 3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.640054945 + -0.5 x = 3.640054945 + -0.5 Combine like terms: 3.640054945 + -0.5 = 3.140054945 x = 3.140054945 Simplifying x = 3.140054945## Subproblem 2

x + 0.5 = -3.640054945 Simplifying x + 0.5 = -3.640054945 Reorder the terms: 0.5 + x = -3.640054945 Solving 0.5 + x = -3.640054945 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 = -3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.640054945 + -0.5 x = -3.640054945 + -0.5 Combine like terms: -3.640054945 + -0.5 = -4.140054945 x = -4.140054945 Simplifying x = -4.140054945## Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.140054945, -4.140054945}

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