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Simplifying 4w2 + 20w + 25 = 225 Reorder the terms: 25 + 20w + 4w2 = 225 Solving 25 + 20w + 4w2 = 225 Solving for variable 'w'. Reorder the terms: 25 + -225 + 20w + 4w2 = 225 + -225 Combine like terms: 25 + -225 = -200 -200 + 20w + 4w2 = 225 + -225 Combine like terms: 225 + -225 = 0 -200 + 20w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-50 + 5w + w2) = 0 Factor a trinomial. 4((-10 + -1w)(5 + -1w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + -1w)' equal to zero and attempt to solve: Simplifying -10 + -1w = 0 Solving -10 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1w = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1w = 0 + 10 -1w = 0 + 10 Combine like terms: 0 + 10 = 10 -1w = 10 Divide each side by '-1'. w = -10 Simplifying w = -10Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 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 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Solution
w = {-10, 5}
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