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Simplifying 20w2 + -45w + 10 = 0 Reorder the terms: 10 + -45w + 20w2 = 0 Solving 10 + -45w + 20w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -9w + 4w2) = 0 Factor a trinomial. 5((1 + -4w)(2 + -1w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -4w)' equal to zero and attempt to solve: Simplifying 1 + -4w = 0 Solving 1 + -4w = 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 + -4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4w = 0 + -1 -4w = 0 + -1 Combine like terms: 0 + -1 = -1 -4w = -1 Divide each side by '-4'. w = 0.25 Simplifying w = 0.25Subproblem 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 = {0.25, 2}
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