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Simplifying x2 + -26x + 124 = 0 Reorder the terms: 124 + -26x + x2 = 0 Solving 124 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-124' to each side of the equation. 124 + -26x + -124 + x2 = 0 + -124 Reorder the terms: 124 + -124 + -26x + x2 = 0 + -124 Combine like terms: 124 + -124 = 0 0 + -26x + x2 = 0 + -124 -26x + x2 = 0 + -124 Combine like terms: 0 + -124 = -124 -26x + x2 = -124 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 = -124 + 169 Reorder the terms: 169 + -26x + x2 = -124 + 169 Combine like terms: -124 + 169 = 45 169 + -26x + x2 = 45 Factor a perfect square on the left side: (x + -13)(x + -13) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -13) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -13 = 6.708203933 Simplifying x + -13 = 6.708203933 Reorder the terms: -13 + x = 6.708203933 Solving -13 + x = 6.708203933 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 = 6.708203933 + 13 Combine like terms: -13 + 13 = 0 0 + x = 6.708203933 + 13 x = 6.708203933 + 13 Combine like terms: 6.708203933 + 13 = 19.708203933 x = 19.708203933 Simplifying x = 19.708203933Subproblem 2
x + -13 = -6.708203933 Simplifying x + -13 = -6.708203933 Reorder the terms: -13 + x = -6.708203933 Solving -13 + x = -6.708203933 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 = -6.708203933 + 13 Combine like terms: -13 + 13 = 0 0 + x = -6.708203933 + 13 x = -6.708203933 + 13 Combine like terms: -6.708203933 + 13 = 6.291796067 x = 6.291796067 Simplifying x = 6.291796067Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.708203933, 6.291796067}
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