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Simplifying x2 + 26x + -169 = 0 Reorder the terms: -169 + 26x + x2 = 0 Solving -169 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '169' to each side of the equation. -169 + 26x + 169 + x2 = 0 + 169 Reorder the terms: -169 + 169 + 26x + x2 = 0 + 169 Combine like terms: -169 + 169 = 0 0 + 26x + x2 = 0 + 169 26x + x2 = 0 + 169 Combine like terms: 0 + 169 = 169 26x + x2 = 169 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 = 169 + 169 Reorder the terms: 169 + 26x + x2 = 169 + 169 Combine like terms: 169 + 169 = 338 169 + 26x + x2 = 338 Factor a perfect square on the left side: (x + 13)(x + 13) = 338 Calculate the square root of the right side: 18.384776311 Break this problem into two subproblems by setting (x + 13) equal to 18.384776311 and -18.384776311.Subproblem 1
x + 13 = 18.384776311 Simplifying x + 13 = 18.384776311 Reorder the terms: 13 + x = 18.384776311 Solving 13 + x = 18.384776311 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 = 18.384776311 + -13 Combine like terms: 13 + -13 = 0 0 + x = 18.384776311 + -13 x = 18.384776311 + -13 Combine like terms: 18.384776311 + -13 = 5.384776311 x = 5.384776311 Simplifying x = 5.384776311Subproblem 2
x + 13 = -18.384776311 Simplifying x + 13 = -18.384776311 Reorder the terms: 13 + x = -18.384776311 Solving 13 + x = -18.384776311 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 = -18.384776311 + -13 Combine like terms: 13 + -13 = 0 0 + x = -18.384776311 + -13 x = -18.384776311 + -13 Combine like terms: -18.384776311 + -13 = -31.384776311 x = -31.384776311 Simplifying x = -31.384776311Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.384776311, -31.384776311}
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