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Simplifying 40 = w(w + -3) Reorder the terms: 40 = w(-3 + w) 40 = (-3 * w + w * w) 40 = (-3w + w2) Solving 40 = -3w + w2 Solving for variable 'w'. Reorder the terms: 40 + 3w + -1w2 = -3w + 3w + w2 + -1w2 Combine like terms: -3w + 3w = 0 40 + 3w + -1w2 = 0 + w2 + -1w2 40 + 3w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 40 + 3w + -1w2 = 0 Factor a trinomial. (8 + -1w)(5 + 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 '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Solution
w = {8, -5}
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