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Simplifying 12w2 = 45 + 51w Solving 12w2 = 45 + 51w Solving for variable 'w'. Reorder the terms: -45 + -51w + 12w2 = 45 + 51w + -45 + -51w Reorder the terms: -45 + -51w + 12w2 = 45 + -45 + 51w + -51w Combine like terms: 45 + -45 = 0 -45 + -51w + 12w2 = 0 + 51w + -51w -45 + -51w + 12w2 = 51w + -51w Combine like terms: 51w + -51w = 0 -45 + -51w + 12w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + -17w + 4w2) = 0 Factor a trinomial. 3((-3 + -4w)(5 + -1w)) = 0 Ignore the factor 3.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 '(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 = {-0.75, 5}
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