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Simplifying 2w2 + 6w + -20 + -1(w2 + 5w) = 52 Reorder the terms: 2w2 + 6w + -20 + -1(5w + w2) = 52 2w2 + 6w + -20 + (5w * -1 + w2 * -1) = 52 2w2 + 6w + -20 + (-5w + -1w2) = 52 Reorder the terms: -20 + 6w + -5w + 2w2 + -1w2 = 52 Combine like terms: 6w + -5w = 1w -20 + 1w + 2w2 + -1w2 = 52 Combine like terms: 2w2 + -1w2 = 1w2 -20 + 1w + 1w2 = 52 Solving -20 + 1w + 1w2 = 52 Solving for variable 'w'. Reorder the terms: -20 + -52 + 1w + 1w2 = 52 + -52 Combine like terms: -20 + -52 = -72 -72 + 1w + 1w2 = 52 + -52 Combine like terms: 52 + -52 = 0 -72 + 1w + 1w2 = 0 Factor a trinomial. (-9 + -1w)(8 + -1w) = 0Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve: Simplifying -9 + -1w = 0 Solving -9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w = 0 + 9 -1w = 0 + 9 Combine like terms: 0 + 9 = 9 -1w = 9 Divide each side by '-1'. w = -9 Simplifying w = -9Subproblem 2
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Solution
w = {-9, 8}
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