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Simplifying 0 = 56w2 + -86w + 20 Reorder the terms: 0 = 20 + -86w + 56w2 Solving 0 = 20 + -86w + 56w2 Solving for variable 'w'. Combine like terms: 0 + -20 = -20 -20 + 86w + -56w2 = 20 + -86w + 56w2 + -20 + 86w + -56w2 Reorder the terms: -20 + 86w + -56w2 = 20 + -20 + -86w + 86w + 56w2 + -56w2 Combine like terms: 20 + -20 = 0 -20 + 86w + -56w2 = 0 + -86w + 86w + 56w2 + -56w2 -20 + 86w + -56w2 = -86w + 86w + 56w2 + -56w2 Combine like terms: -86w + 86w = 0 -20 + 86w + -56w2 = 0 + 56w2 + -56w2 -20 + 86w + -56w2 = 56w2 + -56w2 Combine like terms: 56w2 + -56w2 = 0 -20 + 86w + -56w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 43w + -28w2) = 0 Factor a trinomial. 2((-5 + 4w)(2 + -7w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 4w)' equal to zero and attempt to solve: Simplifying -5 + 4w = 0 Solving -5 + 4w = 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 + 4w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4w = 0 + 5 4w = 0 + 5 Combine like terms: 0 + 5 = 5 4w = 5 Divide each side by '4'. w = 1.25 Simplifying w = 1.25Subproblem 2
Set the factor '(2 + -7w)' equal to zero and attempt to solve: Simplifying 2 + -7w = 0 Solving 2 + -7w = 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 + -7w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7w = 0 + -2 -7w = 0 + -2 Combine like terms: 0 + -2 = -2 -7w = -2 Divide each side by '-7'. w = 0.2857142857 Simplifying w = 0.2857142857Solution
w = {1.25, 0.2857142857}
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