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Simplifying w2 + -2w = 40 + 4w Reorder the terms: -2w + w2 = 40 + 4w Solving -2w + w2 = 40 + 4w Solving for variable 'w'. Reorder the terms: -40 + -2w + -4w + w2 = 40 + 4w + -40 + -4w Combine like terms: -2w + -4w = -6w -40 + -6w + w2 = 40 + 4w + -40 + -4w Reorder the terms: -40 + -6w + w2 = 40 + -40 + 4w + -4w Combine like terms: 40 + -40 = 0 -40 + -6w + w2 = 0 + 4w + -4w -40 + -6w + w2 = 4w + -4w Combine like terms: 4w + -4w = 0 -40 + -6w + w2 = 0 Factor a trinomial. (-4 + -1w)(10 + -1w) = 0Subproblem 1
Set the factor '(-4 + -1w)' equal to zero and attempt to solve: Simplifying -4 + -1w = 0 Solving -4 + -1w = 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 + -1w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1w = 0 + 4 -1w = 0 + 4 Combine like terms: 0 + 4 = 4 -1w = 4 Divide each side by '-1'. w = -4 Simplifying w = -4Subproblem 2
Set the factor '(10 + -1w)' equal to zero and attempt to solve: Simplifying 10 + -1w = 0 Solving 10 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1w = 0 + -10 -1w = 0 + -10 Combine like terms: 0 + -10 = -10 -1w = -10 Divide each side by '-1'. w = 10 Simplifying w = 10Solution
w = {-4, 10}
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