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Simplifying x2 + 26x + 64 = 0 Reorder the terms: 64 + 26x + x2 = 0 Solving 64 + 26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + 26x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + 26x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 26x + x2 = 0 + -64 26x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 26x + x2 = -64 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 = -64 + 169 Reorder the terms: 169 + 26x + x2 = -64 + 169 Combine like terms: -64 + 169 = 105 169 + 26x + x2 = 105 Factor a perfect square on the left side: (x + 13)(x + 13) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + 13) equal to 10.246950766 and -10.246950766.Subproblem 1
x + 13 = 10.246950766 Simplifying x + 13 = 10.246950766 Reorder the terms: 13 + x = 10.246950766 Solving 13 + x = 10.246950766 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 = 10.246950766 + -13 Combine like terms: 13 + -13 = 0 0 + x = 10.246950766 + -13 x = 10.246950766 + -13 Combine like terms: 10.246950766 + -13 = -2.753049234 x = -2.753049234 Simplifying x = -2.753049234Subproblem 2
x + 13 = -10.246950766 Simplifying x + 13 = -10.246950766 Reorder the terms: 13 + x = -10.246950766 Solving 13 + x = -10.246950766 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 = -10.246950766 + -13 Combine like terms: 13 + -13 = 0 0 + x = -10.246950766 + -13 x = -10.246950766 + -13 Combine like terms: -10.246950766 + -13 = -23.246950766 x = -23.246950766 Simplifying x = -23.246950766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.753049234, -23.246950766}
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