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Simplifying 4w2 + 12w + 9 = 25 Reorder the terms: 9 + 12w + 4w2 = 25 Solving 9 + 12w + 4w2 = 25 Solving for variable 'w'. Reorder the terms: 9 + -25 + 12w + 4w2 = 25 + -25 Combine like terms: 9 + -25 = -16 -16 + 12w + 4w2 = 25 + -25 Combine like terms: 25 + -25 = 0 -16 + 12w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 3w + w2) = 0 Factor a trinomial. 4((-4 + -1w)(1 + -1w)) = 0 Ignore the factor 4.Subproblem 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 '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Solution
w = {-4, 1}
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