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Simplifying 4w2 + 30w = 54 Reorder the terms: 30w + 4w2 = 54 Solving 30w + 4w2 = 54 Solving for variable 'w'. Reorder the terms: -54 + 30w + 4w2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + 30w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 15w + 2w2) = 0 Factor a trinomial. 2((-9 + -1w)(3 + -2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve: Simplifying -9 + -1w = 0 Solving -9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w = 0 + 9 -1w = 0 + 9 Combine like terms: 0 + 9 = 9 -1w = 9 Divide each side by '-1'. w = -9 Simplifying w = -9Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 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 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5Solution
w = {-9, 1.5}
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