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Simplifying (5w + -5)(5w + -5) = 0 Reorder the terms: (-5 + 5w)(5w + -5) = 0 Reorder the terms: (-5 + 5w)(-5 + 5w) = 0 Multiply (-5 + 5w) * (-5 + 5w) (-5(-5 + 5w) + 5w * (-5 + 5w)) = 0 ((-5 * -5 + 5w * -5) + 5w * (-5 + 5w)) = 0 ((25 + -25w) + 5w * (-5 + 5w)) = 0 (25 + -25w + (-5 * 5w + 5w * 5w)) = 0 (25 + -25w + (-25w + 25w2)) = 0 Combine like terms: -25w + -25w = -50w (25 + -50w + 25w2) = 0 Solving 25 + -50w + 25w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '25'. 25(1 + -2w + w2) = 0 Factor a trinomial. 25((1 + -1w)(1 + -1w)) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Solution
w = {1, 1}
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