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Simplifying 4w2 + 12w + 9 = 49 Reorder the terms: 9 + 12w + 4w2 = 49 Solving 9 + 12w + 4w2 = 49 Solving for variable 'w'. Reorder the terms: 9 + -49 + 12w + 4w2 = 49 + -49 Combine like terms: 9 + -49 = -40 -40 + 12w + 4w2 = 49 + -49 Combine like terms: 49 + -49 = 0 -40 + 12w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + 3w + w2) = 0 Factor a trinomial. 4((-5 + -1w)(2 + -1w)) = 0 Ignore the factor 4.Subproblem 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 '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Solution
w = {-5, 2}
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