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Simplifying x2 + 26x + 112 = 0 Reorder the terms: 112 + 26x + x2 = 0 Solving 112 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-112' to each side of the equation. 112 + 26x + -112 + x2 = 0 + -112 Reorder the terms: 112 + -112 + 26x + x2 = 0 + -112 Combine like terms: 112 + -112 = 0 0 + 26x + x2 = 0 + -112 26x + x2 = 0 + -112 Combine like terms: 0 + -112 = -112 26x + x2 = -112 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 = -112 + 169 Reorder the terms: 169 + 26x + x2 = -112 + 169 Combine like terms: -112 + 169 = 57 169 + 26x + x2 = 57 Factor a perfect square on the left side: (x + 13)(x + 13) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + 13) equal to 7.549834435 and -7.549834435.Subproblem 1
x + 13 = 7.549834435 Simplifying x + 13 = 7.549834435 Reorder the terms: 13 + x = 7.549834435 Solving 13 + x = 7.549834435 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 = 7.549834435 + -13 Combine like terms: 13 + -13 = 0 0 + x = 7.549834435 + -13 x = 7.549834435 + -13 Combine like terms: 7.549834435 + -13 = -5.450165565 x = -5.450165565 Simplifying x = -5.450165565Subproblem 2
x + 13 = -7.549834435 Simplifying x + 13 = -7.549834435 Reorder the terms: 13 + x = -7.549834435 Solving 13 + x = -7.549834435 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 = -7.549834435 + -13 Combine like terms: 13 + -13 = 0 0 + x = -7.549834435 + -13 x = -7.549834435 + -13 Combine like terms: -7.549834435 + -13 = -20.549834435 x = -20.549834435 Simplifying x = -20.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.450165565, -20.549834435}
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