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Simplifying 16w2 = 36 + 36w Solving 16w2 = 36 + 36w Solving for variable 'w'. Reorder the terms: -36 + -36w + 16w2 = 36 + 36w + -36 + -36w Reorder the terms: -36 + -36w + 16w2 = 36 + -36 + 36w + -36w Combine like terms: 36 + -36 = 0 -36 + -36w + 16w2 = 0 + 36w + -36w -36 + -36w + 16w2 = 36w + -36w Combine like terms: 36w + -36w = 0 -36 + -36w + 16w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -9w + 4w2) = 0 Factor a trinomial. 4((-3 + -4w)(3 + -1w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -4w)' equal to zero and attempt to solve: Simplifying -3 + -4w = 0 Solving -3 + -4w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4w = 0 + 3 -4w = 0 + 3 Combine like terms: 0 + 3 = 3 -4w = 3 Divide each side by '-4'. w = -0.75 Simplifying w = -0.75Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3Solution
w = {-0.75, 3}
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