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Simplifying (8 + w)(4 + w) = 252 Multiply (8 + w) * (4 + w) (8(4 + w) + w(4 + w)) = 252 ((4 * 8 + w * 8) + w(4 + w)) = 252 ((32 + 8w) + w(4 + w)) = 252 (32 + 8w + (4 * w + w * w)) = 252 (32 + 8w + (4w + w2)) = 252 Combine like terms: 8w + 4w = 12w (32 + 12w + w2) = 252 Solving 32 + 12w + w2 = 252 Solving for variable 'w'. Reorder the terms: 32 + -252 + 12w + w2 = 252 + -252 Combine like terms: 32 + -252 = -220 -220 + 12w + w2 = 252 + -252 Combine like terms: 252 + -252 = 0 -220 + 12w + w2 = 0 Factor a trinomial. (-22 + -1w)(10 + -1w) = 0Subproblem 1
Set the factor '(-22 + -1w)' equal to zero and attempt to solve: Simplifying -22 + -1w = 0 Solving -22 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + -1w = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -1w = 0 + 22 -1w = 0 + 22 Combine like terms: 0 + 22 = 22 -1w = 22 Divide each side by '-1'. w = -22 Simplifying w = -22Subproblem 2
Set the factor '(10 + -1w)' equal to zero and attempt to solve: Simplifying 10 + -1w = 0 Solving 10 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1w = 0 + -10 -1w = 0 + -10 Combine like terms: 0 + -10 = -10 -1w = -10 Divide each side by '-1'. w = 10 Simplifying w = 10Solution
w = {-22, 10}
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