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Simplifying ((w + -2)(2w + 10)) + -1(w(w + 5)) = 220 Reorder the terms: ((-2 + w)(2w + 10)) + -1(w(w + 5)) = 220 Reorder the terms: ((-2 + w)(10 + 2w)) + -1(w(w + 5)) = 220 Multiply (-2 + w) * (10 + 2w) ((-2(10 + 2w) + w(10 + 2w))) + -1(w(w + 5)) = 220 (((10 * -2 + 2w * -2) + w(10 + 2w))) + -1(w(w + 5)) = 220 (((-20 + -4w) + w(10 + 2w))) + -1(w(w + 5)) = 220 ((-20 + -4w + (10 * w + 2w * w))) + -1(w(w + 5)) = 220 ((-20 + -4w + (10w + 2w2))) + -1(w(w + 5)) = 220 Combine like terms: -4w + 10w = 6w ((-20 + 6w + 2w2)) + -1(w(w + 5)) = 220 (-20 + 6w + 2w2) + -1(w(w + 5)) = 220 Remove parenthesis around (-20 + 6w + 2w2) -20 + 6w + 2w2 + -1(w(w + 5)) = 220 Reorder the terms: -20 + 6w + 2w2 + -1(w(5 + w)) = 220 -20 + 6w + 2w2 + -1((5 * w + w * w)) = 220 -20 + 6w + 2w2 + -1((5w + w2)) = 220 -20 + 6w + 2w2 + (5w * -1 + w2 * -1) = 220 -20 + 6w + 2w2 + (-5w + -1w2) = 220 Reorder the terms: -20 + 6w + -5w + 2w2 + -1w2 = 220 Combine like terms: 6w + -5w = 1w -20 + 1w + 2w2 + -1w2 = 220 Combine like terms: 2w2 + -1w2 = 1w2 -20 + 1w + 1w2 = 220 Solving -20 + 1w + 1w2 = 220 Solving for variable 'w'. Reorder the terms: -20 + -220 + 1w + 1w2 = 220 + -220 Combine like terms: -20 + -220 = -240 -240 + 1w + 1w2 = 220 + -220 Combine like terms: 220 + -220 = 0 -240 + 1w + 1w2 = 0 Factor a trinomial. (-16 + -1w)(15 + -1w) = 0Subproblem 1
Set the factor '(-16 + -1w)' equal to zero and attempt to solve: Simplifying -16 + -1w = 0 Solving -16 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -1w = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -1w = 0 + 16 -1w = 0 + 16 Combine like terms: 0 + 16 = 16 -1w = 16 Divide each side by '-1'. w = -16 Simplifying w = -16Subproblem 2
Set the factor '(15 + -1w)' equal to zero and attempt to solve: Simplifying 15 + -1w = 0 Solving 15 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1w = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1w = 0 + -15 -1w = 0 + -15 Combine like terms: 0 + -15 = -15 -1w = -15 Divide each side by '-1'. w = 15 Simplifying w = 15Solution
w = {-16, 15}
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