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Simplifying x2 + 26x + 108 = 0 Reorder the terms: 108 + 26x + x2 = 0 Solving 108 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-108' to each side of the equation. 108 + 26x + -108 + x2 = 0 + -108 Reorder the terms: 108 + -108 + 26x + x2 = 0 + -108 Combine like terms: 108 + -108 = 0 0 + 26x + x2 = 0 + -108 26x + x2 = 0 + -108 Combine like terms: 0 + -108 = -108 26x + x2 = -108 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -108 + 169 Reorder the terms: 169 + 26x + x2 = -108 + 169 Combine like terms: -108 + 169 = 61 169 + 26x + x2 = 61 Factor a perfect square on the left side: (x + 13)(x + 13) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + 13) equal to 7.810249676 and -7.810249676.Subproblem 1
x + 13 = 7.810249676 Simplifying x + 13 = 7.810249676 Reorder the terms: 13 + x = 7.810249676 Solving 13 + x = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 7.810249676 + -13 Combine like terms: 13 + -13 = 0 0 + x = 7.810249676 + -13 x = 7.810249676 + -13 Combine like terms: 7.810249676 + -13 = -5.189750324 x = -5.189750324 Simplifying x = -5.189750324Subproblem 2
x + 13 = -7.810249676 Simplifying x + 13 = -7.810249676 Reorder the terms: 13 + x = -7.810249676 Solving 13 + x = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -7.810249676 + -13 Combine like terms: 13 + -13 = 0 0 + x = -7.810249676 + -13 x = -7.810249676 + -13 Combine like terms: -7.810249676 + -13 = -20.810249676 x = -20.810249676 Simplifying x = -20.810249676Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.189750324, -20.810249676}
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