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Simplifying x2 + 26x + -85 = 0 Reorder the terms: -85 + 26x + x2 = 0 Solving -85 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + 26x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + 26x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 26x + x2 = 0 + 85 26x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 26x + x2 = 85 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 = 85 + 169 Reorder the terms: 169 + 26x + x2 = 85 + 169 Combine like terms: 85 + 169 = 254 169 + 26x + x2 = 254 Factor a perfect square on the left side: (x + 13)(x + 13) = 254 Calculate the square root of the right side: 15.937377451 Break this problem into two subproblems by setting (x + 13) equal to 15.937377451 and -15.937377451.Subproblem 1
x + 13 = 15.937377451 Simplifying x + 13 = 15.937377451 Reorder the terms: 13 + x = 15.937377451 Solving 13 + x = 15.937377451 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 = 15.937377451 + -13 Combine like terms: 13 + -13 = 0 0 + x = 15.937377451 + -13 x = 15.937377451 + -13 Combine like terms: 15.937377451 + -13 = 2.937377451 x = 2.937377451 Simplifying x = 2.937377451Subproblem 2
x + 13 = -15.937377451 Simplifying x + 13 = -15.937377451 Reorder the terms: 13 + x = -15.937377451 Solving 13 + x = -15.937377451 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 = -15.937377451 + -13 Combine like terms: 13 + -13 = 0 0 + x = -15.937377451 + -13 x = -15.937377451 + -13 Combine like terms: -15.937377451 + -13 = -28.937377451 x = -28.937377451 Simplifying x = -28.937377451Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.937377451, -28.937377451}
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