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Simplifying x2 + 26x + 59 = 0 Reorder the terms: 59 + 26x + x2 = 0 Solving 59 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 26x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 26x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 26x + x2 = 0 + -59 26x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 26x + x2 = -59 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 = -59 + 169 Reorder the terms: 169 + 26x + x2 = -59 + 169 Combine like terms: -59 + 169 = 110 169 + 26x + x2 = 110 Factor a perfect square on the left side: (x + 13)(x + 13) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (x + 13) equal to 10.488088482 and -10.488088482.Subproblem 1
x + 13 = 10.488088482 Simplifying x + 13 = 10.488088482 Reorder the terms: 13 + x = 10.488088482 Solving 13 + x = 10.488088482 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 = 10.488088482 + -13 Combine like terms: 13 + -13 = 0 0 + x = 10.488088482 + -13 x = 10.488088482 + -13 Combine like terms: 10.488088482 + -13 = -2.511911518 x = -2.511911518 Simplifying x = -2.511911518Subproblem 2
x + 13 = -10.488088482 Simplifying x + 13 = -10.488088482 Reorder the terms: 13 + x = -10.488088482 Solving 13 + x = -10.488088482 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 = -10.488088482 + -13 Combine like terms: 13 + -13 = 0 0 + x = -10.488088482 + -13 x = -10.488088482 + -13 Combine like terms: -10.488088482 + -13 = -23.488088482 x = -23.488088482 Simplifying x = -23.488088482Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.511911518, -23.488088482}
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