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Simplifying 20w2 = 64 + 64w Solving 20w2 = 64 + 64w Solving for variable 'w'. Reorder the terms: -64 + -64w + 20w2 = 64 + 64w + -64 + -64w Reorder the terms: -64 + -64w + 20w2 = 64 + -64 + 64w + -64w Combine like terms: 64 + -64 = 0 -64 + -64w + 20w2 = 0 + 64w + -64w -64 + -64w + 20w2 = 64w + -64w Combine like terms: 64w + -64w = 0 -64 + -64w + 20w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-16 + -16w + 5w2) = 0 Factor a trinomial. 4((-4 + -5w)(4 + -1w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -5w)' equal to zero and attempt to solve: Simplifying -4 + -5w = 0 Solving -4 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5w = 0 + 4 -5w = 0 + 4 Combine like terms: 0 + 4 = 4 -5w = 4 Divide each side by '-5'. w = -0.8 Simplifying w = -0.8Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Solution
w = {-0.8, 4}
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