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Simplifying x2 + 26x = 88 Reorder the terms: 26x + x2 = 88 Solving 26x + x2 = 88 Solving for variable 'x'. Reorder the terms: -88 + 26x + x2 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + 26x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 26x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 26x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 26x + x2 = 0 + 88 26x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 26x + x2 = 88 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 = 88 + 169 Reorder the terms: 169 + 26x + x2 = 88 + 169 Combine like terms: 88 + 169 = 257 169 + 26x + x2 = 257 Factor a perfect square on the left side: (x + 13)(x + 13) = 257 Calculate the square root of the right side: 16.031219542 Break this problem into two subproblems by setting (x + 13) equal to 16.031219542 and -16.031219542.Subproblem 1
x + 13 = 16.031219542 Simplifying x + 13 = 16.031219542 Reorder the terms: 13 + x = 16.031219542 Solving 13 + x = 16.031219542 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 = 16.031219542 + -13 Combine like terms: 13 + -13 = 0 0 + x = 16.031219542 + -13 x = 16.031219542 + -13 Combine like terms: 16.031219542 + -13 = 3.031219542 x = 3.031219542 Simplifying x = 3.031219542Subproblem 2
x + 13 = -16.031219542 Simplifying x + 13 = -16.031219542 Reorder the terms: 13 + x = -16.031219542 Solving 13 + x = -16.031219542 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 = -16.031219542 + -13 Combine like terms: 13 + -13 = 0 0 + x = -16.031219542 + -13 x = -16.031219542 + -13 Combine like terms: -16.031219542 + -13 = -29.031219542 x = -29.031219542 Simplifying x = -29.031219542Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.031219542, -29.031219542}
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