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Simplifying 4w2 + 72w + -76 = 0 Reorder the terms: -76 + 72w + 4w2 = 0 Solving -76 + 72w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(-19 + 18w + w2) = 0 Factor a trinomial. 4((-19 + -1w)(1 + -1w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-19 + -1w)' equal to zero and attempt to solve: Simplifying -19 + -1w = 0 Solving -19 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -1w = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -1w = 0 + 19 -1w = 0 + 19 Combine like terms: 0 + 19 = 19 -1w = 19 Divide each side by '-1'. w = -19 Simplifying w = -19Subproblem 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 = {-19, 1}
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