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Simplifying (2x + 39)(x + 64) = 180 Reorder the terms: (39 + 2x)(x + 64) = 180 Reorder the terms: (39 + 2x)(64 + x) = 180 Multiply (39 + 2x) * (64 + x) (39(64 + x) + 2x * (64 + x)) = 180 ((64 * 39 + x * 39) + 2x * (64 + x)) = 180 ((2496 + 39x) + 2x * (64 + x)) = 180 (2496 + 39x + (64 * 2x + x * 2x)) = 180 (2496 + 39x + (128x + 2x2)) = 180 Combine like terms: 39x + 128x = 167x (2496 + 167x + 2x2) = 180 Solving 2496 + 167x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: 2496 + -180 + 167x + 2x2 = 180 + -180 Combine like terms: 2496 + -180 = 2316 2316 + 167x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 2316 + 167x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1158 + 83.5x + x2 = 0 Move the constant term to the right: Add '-1158' to each side of the equation. 1158 + 83.5x + -1158 + x2 = 0 + -1158 Reorder the terms: 1158 + -1158 + 83.5x + x2 = 0 + -1158 Combine like terms: 1158 + -1158 = 0 0 + 83.5x + x2 = 0 + -1158 83.5x + x2 = 0 + -1158 Combine like terms: 0 + -1158 = -1158 83.5x + x2 = -1158 The x term is 83.5x. Take half its coefficient (41.75). Square it (1743.0625) and add it to both sides. Add '1743.0625' to each side of the equation. 83.5x + 1743.0625 + x2 = -1158 + 1743.0625 Reorder the terms: 1743.0625 + 83.5x + x2 = -1158 + 1743.0625 Combine like terms: -1158 + 1743.0625 = 585.0625 1743.0625 + 83.5x + x2 = 585.0625 Factor a perfect square on the left side: (x + 41.75)(x + 41.75) = 585.0625 Calculate the square root of the right side: 24.188065239 Break this problem into two subproblems by setting (x + 41.75) equal to 24.188065239 and -24.188065239.Subproblem 1
x + 41.75 = 24.188065239 Simplifying x + 41.75 = 24.188065239 Reorder the terms: 41.75 + x = 24.188065239 Solving 41.75 + x = 24.188065239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-41.75' to each side of the equation. 41.75 + -41.75 + x = 24.188065239 + -41.75 Combine like terms: 41.75 + -41.75 = 0.00 0.00 + x = 24.188065239 + -41.75 x = 24.188065239 + -41.75 Combine like terms: 24.188065239 + -41.75 = -17.561934761 x = -17.561934761 Simplifying x = -17.561934761Subproblem 2
x + 41.75 = -24.188065239 Simplifying x + 41.75 = -24.188065239 Reorder the terms: 41.75 + x = -24.188065239 Solving 41.75 + x = -24.188065239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-41.75' to each side of the equation. 41.75 + -41.75 + x = -24.188065239 + -41.75 Combine like terms: 41.75 + -41.75 = 0.00 0.00 + x = -24.188065239 + -41.75 x = -24.188065239 + -41.75 Combine like terms: -24.188065239 + -41.75 = -65.938065239 x = -65.938065239 Simplifying x = -65.938065239Solution
The solution to the problem is based on the solutions from the subproblems. x = {-17.561934761, -65.938065239}
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