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Simplifying 4w2 + 12w + 9 = 169 Reorder the terms: 9 + 12w + 4w2 = 169 Solving 9 + 12w + 4w2 = 169 Solving for variable 'w'. Reorder the terms: 9 + -169 + 12w + 4w2 = 169 + -169 Combine like terms: 9 + -169 = -160 -160 + 12w + 4w2 = 169 + -169 Combine like terms: 169 + -169 = 0 -160 + 12w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-40 + 3w + w2) = 0 Factor a trinomial. 4((-8 + -1w)(5 + -1w)) = 0 Ignore the factor 4.Subproblem 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 + -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 = 5Solution
w = {-8, 5}
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