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Simplifying (12 + x)(20 + x) = 360 Multiply (12 + x) * (20 + x) (12(20 + x) + x(20 + x)) = 360 ((20 * 12 + x * 12) + x(20 + x)) = 360 ((240 + 12x) + x(20 + x)) = 360 (240 + 12x + (20 * x + x * x)) = 360 (240 + 12x + (20x + x2)) = 360 Combine like terms: 12x + 20x = 32x (240 + 32x + x2) = 360 Solving 240 + 32x + x2 = 360 Solving for variable 'x'. Reorder the terms: 240 + -360 + 32x + x2 = 360 + -360 Combine like terms: 240 + -360 = -120 -120 + 32x + x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -120 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 32x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 32x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 32x + x2 = 0 + 120 32x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 32x + x2 = 120 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = 120 + 256 Reorder the terms: 256 + 32x + x2 = 120 + 256 Combine like terms: 120 + 256 = 376 256 + 32x + x2 = 376 Factor a perfect square on the left side: (x + 16)(x + 16) = 376 Calculate the square root of the right side: 19.39071943 Break this problem into two subproblems by setting (x + 16) equal to 19.39071943 and -19.39071943.Subproblem 1
x + 16 = 19.39071943 Simplifying x + 16 = 19.39071943 Reorder the terms: 16 + x = 19.39071943 Solving 16 + x = 19.39071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 19.39071943 + -16 Combine like terms: 16 + -16 = 0 0 + x = 19.39071943 + -16 x = 19.39071943 + -16 Combine like terms: 19.39071943 + -16 = 3.39071943 x = 3.39071943 Simplifying x = 3.39071943Subproblem 2
x + 16 = -19.39071943 Simplifying x + 16 = -19.39071943 Reorder the terms: 16 + x = -19.39071943 Solving 16 + x = -19.39071943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -19.39071943 + -16 Combine like terms: 16 + -16 = 0 0 + x = -19.39071943 + -16 x = -19.39071943 + -16 Combine like terms: -19.39071943 + -16 = -35.39071943 x = -35.39071943 Simplifying x = -35.39071943Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.39071943, -35.39071943}
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