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Simplifying (x + 66)(2x + -8) = 180 Reorder the terms: (66 + x)(2x + -8) = 180 Reorder the terms: (66 + x)(-8 + 2x) = 180 Multiply (66 + x) * (-8 + 2x) (66(-8 + 2x) + x(-8 + 2x)) = 180 ((-8 * 66 + 2x * 66) + x(-8 + 2x)) = 180 ((-528 + 132x) + x(-8 + 2x)) = 180 (-528 + 132x + (-8 * x + 2x * x)) = 180 (-528 + 132x + (-8x + 2x2)) = 180 Combine like terms: 132x + -8x = 124x (-528 + 124x + 2x2) = 180 Solving -528 + 124x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -528 + -180 + 124x + 2x2 = 180 + -180 Combine like terms: -528 + -180 = -708 -708 + 124x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -708 + 124x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-354 + 62x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-354 + 62x + x2)' equal to zero and attempt to solve: Simplifying -354 + 62x + x2 = 0 Solving -354 + 62x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '354' to each side of the equation. -354 + 62x + 354 + x2 = 0 + 354 Reorder the terms: -354 + 354 + 62x + x2 = 0 + 354 Combine like terms: -354 + 354 = 0 0 + 62x + x2 = 0 + 354 62x + x2 = 0 + 354 Combine like terms: 0 + 354 = 354 62x + x2 = 354 The x term is 62x. Take half its coefficient (31). Square it (961) and add it to both sides. Add '961' to each side of the equation. 62x + 961 + x2 = 354 + 961 Reorder the terms: 961 + 62x + x2 = 354 + 961 Combine like terms: 354 + 961 = 1315 961 + 62x + x2 = 1315 Factor a perfect square on the left side: (x + 31)(x + 31) = 1315 Calculate the square root of the right side: 36.262928729 Break this problem into two subproblems by setting (x + 31) equal to 36.262928729 and -36.262928729.Subproblem 1
x + 31 = 36.262928729 Simplifying x + 31 = 36.262928729 Reorder the terms: 31 + x = 36.262928729 Solving 31 + x = 36.262928729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = 36.262928729 + -31 Combine like terms: 31 + -31 = 0 0 + x = 36.262928729 + -31 x = 36.262928729 + -31 Combine like terms: 36.262928729 + -31 = 5.262928729 x = 5.262928729 Simplifying x = 5.262928729Subproblem 2
x + 31 = -36.262928729 Simplifying x + 31 = -36.262928729 Reorder the terms: 31 + x = -36.262928729 Solving 31 + x = -36.262928729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = -36.262928729 + -31 Combine like terms: 31 + -31 = 0 0 + x = -36.262928729 + -31 x = -36.262928729 + -31 Combine like terms: -36.262928729 + -31 = -67.262928729 x = -67.262928729 Simplifying x = -67.262928729Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.262928729, -67.262928729}Solution
x = {5.262928729, -67.262928729}
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