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Simplifying (w + -3)(w + -3) = -2w + 54 Reorder the terms: (-3 + w)(w + -3) = -2w + 54 Reorder the terms: (-3 + w)(-3 + w) = -2w + 54 Multiply (-3 + w) * (-3 + w) (-3(-3 + w) + w(-3 + w)) = -2w + 54 ((-3 * -3 + w * -3) + w(-3 + w)) = -2w + 54 ((9 + -3w) + w(-3 + w)) = -2w + 54 (9 + -3w + (-3 * w + w * w)) = -2w + 54 (9 + -3w + (-3w + w2)) = -2w + 54 Combine like terms: -3w + -3w = -6w (9 + -6w + w2) = -2w + 54 Reorder the terms: 9 + -6w + w2 = 54 + -2w Solving 9 + -6w + w2 = 54 + -2w Solving for variable 'w'. Reorder the terms: 9 + -54 + -6w + 2w + w2 = 54 + -2w + -54 + 2w Combine like terms: 9 + -54 = -45 -45 + -6w + 2w + w2 = 54 + -2w + -54 + 2w Combine like terms: -6w + 2w = -4w -45 + -4w + w2 = 54 + -2w + -54 + 2w Reorder the terms: -45 + -4w + w2 = 54 + -54 + -2w + 2w Combine like terms: 54 + -54 = 0 -45 + -4w + w2 = 0 + -2w + 2w -45 + -4w + w2 = -2w + 2w Combine like terms: -2w + 2w = 0 -45 + -4w + w2 = 0 Factor a trinomial. (-5 + -1w)(9 + -1w) = 0Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve: Simplifying -5 + -1w = 0 Solving -5 + -1w = 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 + -1w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1w = 0 + 5 -1w = 0 + 5 Combine like terms: 0 + 5 = 5 -1w = 5 Divide each side by '-1'. w = -5 Simplifying w = -5Subproblem 2
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 = 9Solution
w = {-5, 9}
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