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Simplifying 26x + -1x2 = 108 Solving 26x + -1x2 = 108 Solving for variable 'x'. Reorder the terms: -108 + 26x + -1x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + 26x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 108 + -26x + x2 = 0 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 = 20.810249676 x = 20.810249676 Simplifying x = 20.810249676Subproblem 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 = 5.189750324 x = 5.189750324 Simplifying x = 5.189750324Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.810249676, 5.189750324}
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