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Simplifying (w + 12)(w + 20) = 360 Reorder the terms: (12 + w)(w + 20) = 360 Reorder the terms: (12 + w)(20 + w) = 360 Multiply (12 + w) * (20 + w) (12(20 + w) + w(20 + w)) = 360 ((20 * 12 + w * 12) + w(20 + w)) = 360 ((240 + 12w) + w(20 + w)) = 360 (240 + 12w + (20 * w + w * w)) = 360 (240 + 12w + (20w + w2)) = 360 Combine like terms: 12w + 20w = 32w (240 + 32w + w2) = 360 Solving 240 + 32w + w2 = 360 Solving for variable 'w'. Reorder the terms: 240 + -360 + 32w + w2 = 360 + -360 Combine like terms: 240 + -360 = -120 -120 + 32w + w2 = 360 + -360 Combine like terms: 360 + -360 = 0 -120 + 32w + w2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 32w + 120 + w2 = 0 + 120 Reorder the terms: -120 + 120 + 32w + w2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 32w + w2 = 0 + 120 32w + w2 = 0 + 120 Combine like terms: 0 + 120 = 120 32w + w2 = 120 The w term is 32w. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32w + 256 + w2 = 120 + 256 Reorder the terms: 256 + 32w + w2 = 120 + 256 Combine like terms: 120 + 256 = 376 256 + 32w + w2 = 376 Factor a perfect square on the left side: (w + 16)(w + 16) = 376 Calculate the square root of the right side: 19.39071943 Break this problem into two subproblems by setting (w + 16) equal to 19.39071943 and -19.39071943.Subproblem 1
w + 16 = 19.39071943 Simplifying w + 16 = 19.39071943 Reorder the terms: 16 + w = 19.39071943 Solving 16 + w = 19.39071943 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + w = 19.39071943 + -16 Combine like terms: 16 + -16 = 0 0 + w = 19.39071943 + -16 w = 19.39071943 + -16 Combine like terms: 19.39071943 + -16 = 3.39071943 w = 3.39071943 Simplifying w = 3.39071943Subproblem 2
w + 16 = -19.39071943 Simplifying w + 16 = -19.39071943 Reorder the terms: 16 + w = -19.39071943 Solving 16 + w = -19.39071943 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + w = -19.39071943 + -16 Combine like terms: 16 + -16 = 0 0 + w = -19.39071943 + -16 w = -19.39071943 + -16 Combine like terms: -19.39071943 + -16 = -35.39071943 w = -35.39071943 Simplifying w = -35.39071943Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.39071943, -35.39071943}
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