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Simplifying x2 + 26x + -118 = 0 Reorder the terms: -118 + 26x + x2 = 0 Solving -118 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '118' to each side of the equation. -118 + 26x + 118 + x2 = 0 + 118 Reorder the terms: -118 + 118 + 26x + x2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 26x + x2 = 0 + 118 26x + x2 = 0 + 118 Combine like terms: 0 + 118 = 118 26x + x2 = 118 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 = 118 + 169 Reorder the terms: 169 + 26x + x2 = 118 + 169 Combine like terms: 118 + 169 = 287 169 + 26x + x2 = 287 Factor a perfect square on the left side: (x + 13)(x + 13) = 287 Calculate the square root of the right side: 16.941074346 Break this problem into two subproblems by setting (x + 13) equal to 16.941074346 and -16.941074346.Subproblem 1
x + 13 = 16.941074346 Simplifying x + 13 = 16.941074346 Reorder the terms: 13 + x = 16.941074346 Solving 13 + x = 16.941074346 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 = 16.941074346 + -13 Combine like terms: 13 + -13 = 0 0 + x = 16.941074346 + -13 x = 16.941074346 + -13 Combine like terms: 16.941074346 + -13 = 3.941074346 x = 3.941074346 Simplifying x = 3.941074346Subproblem 2
x + 13 = -16.941074346 Simplifying x + 13 = -16.941074346 Reorder the terms: 13 + x = -16.941074346 Solving 13 + x = -16.941074346 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 = -16.941074346 + -13 Combine like terms: 13 + -13 = 0 0 + x = -16.941074346 + -13 x = -16.941074346 + -13 Combine like terms: -16.941074346 + -13 = -29.941074346 x = -29.941074346 Simplifying x = -29.941074346Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.941074346, -29.941074346}
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