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