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Simplifying 3w2 + 20w + 144 = 2w2 + -4w Reorder the terms: 144 + 20w + 3w2 = 2w2 + -4w Reorder the terms: 144 + 20w + 3w2 = -4w + 2w2 Solving 144 + 20w + 3w2 = -4w + 2w2 Solving for variable 'w'. Reorder the terms: 144 + 20w + 4w + 3w2 + -2w2 = -4w + 2w2 + 4w + -2w2 Combine like terms: 20w + 4w = 24w 144 + 24w + 3w2 + -2w2 = -4w + 2w2 + 4w + -2w2 Combine like terms: 3w2 + -2w2 = 1w2 144 + 24w + 1w2 = -4w + 2w2 + 4w + -2w2 Reorder the terms: 144 + 24w + 1w2 = -4w + 4w + 2w2 + -2w2 Combine like terms: -4w + 4w = 0 144 + 24w + 1w2 = 0 + 2w2 + -2w2 144 + 24w + 1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 144 + 24w + 1w2 = 0 Factor a trinomial. (12 + w)(12 + w) = 0Subproblem 1
Set the factor '(12 + w)' equal to zero and attempt to solve: Simplifying 12 + w = 0 Solving 12 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + w = 0 + -12 Combine like terms: 12 + -12 = 0 0 + w = 0 + -12 w = 0 + -12 Combine like terms: 0 + -12 = -12 w = -12 Simplifying w = -12Subproblem 2
Set the factor '(12 + w)' equal to zero and attempt to solve: Simplifying 12 + w = 0 Solving 12 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + w = 0 + -12 Combine like terms: 12 + -12 = 0 0 + w = 0 + -12 w = 0 + -12 Combine like terms: 0 + -12 = -12 w = -12 Simplifying w = -12Solution
w = {-12, -12}
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