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Simplifying x2 + -26x = -56 Reorder the terms: -26x + x2 = -56 Solving -26x + x2 = -56 Solving for variable 'x'. Reorder the terms: 56 + -26x + x2 = -56 + 56 Combine like terms: -56 + 56 = 0 56 + -26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + -26x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + -26x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -26x + x2 = 0 + -56 -26x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 -26x + x2 = -56 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 = -56 + 169 Reorder the terms: 169 + -26x + x2 = -56 + 169 Combine like terms: -56 + 169 = 113 169 + -26x + x2 = 113 Factor a perfect square on the left side: (x + -13)(x + -13) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x + -13) equal to 10.630145813 and -10.630145813.Subproblem 1
x + -13 = 10.630145813 Simplifying x + -13 = 10.630145813 Reorder the terms: -13 + x = 10.630145813 Solving -13 + x = 10.630145813 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 = 10.630145813 + 13 Combine like terms: -13 + 13 = 0 0 + x = 10.630145813 + 13 x = 10.630145813 + 13 Combine like terms: 10.630145813 + 13 = 23.630145813 x = 23.630145813 Simplifying x = 23.630145813Subproblem 2
x + -13 = -10.630145813 Simplifying x + -13 = -10.630145813 Reorder the terms: -13 + x = -10.630145813 Solving -13 + x = -10.630145813 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 = -10.630145813 + 13 Combine like terms: -13 + 13 = 0 0 + x = -10.630145813 + 13 x = -10.630145813 + 13 Combine like terms: -10.630145813 + 13 = 2.369854187 x = 2.369854187 Simplifying x = 2.369854187Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.630145813, 2.369854187}
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