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Simplifying 4w2 + 4w + 1 = 25 Reorder the terms: 1 + 4w + 4w2 = 25 Solving 1 + 4w + 4w2 = 25 Solving for variable 'w'. Reorder the terms: 1 + -25 + 4w + 4w2 = 25 + -25 Combine like terms: 1 + -25 = -24 -24 + 4w + 4w2 = 25 + -25 Combine like terms: 25 + -25 = 0 -24 + 4w + 4w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + w + w2) = 0 Factor a trinomial. 4((-3 + -1w)(2 + -1w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 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 = {-3, 2}
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