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Simplifying 21 = w(w + -4) Reorder the terms: 21 = w(-4 + w) 21 = (-4 * w + w * w) 21 = (-4w + w2) Solving 21 = -4w + w2 Solving for variable 'w'. Reorder the terms: 21 + 4w + -1w2 = -4w + 4w + w2 + -1w2 Combine like terms: -4w + 4w = 0 21 + 4w + -1w2 = 0 + w2 + -1w2 21 + 4w + -1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 21 + 4w + -1w2 = 0 Factor a trinomial. (7 + -1w)(3 + w) = 0Subproblem 1
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3Solution
w = {7, -3}
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