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Simplifying (w + -5)(2w + -5) = 0 Reorder the terms: (-5 + w)(2w + -5) = 0 Reorder the terms: (-5 + w)(-5 + 2w) = 0 Multiply (-5 + w) * (-5 + 2w) (-5(-5 + 2w) + w(-5 + 2w)) = 0 ((-5 * -5 + 2w * -5) + w(-5 + 2w)) = 0 ((25 + -10w) + w(-5 + 2w)) = 0 (25 + -10w + (-5 * w + 2w * w)) = 0 (25 + -10w + (-5w + 2w2)) = 0 Combine like terms: -10w + -5w = -15w (25 + -15w + 2w2) = 0 Solving 25 + -15w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (5 + -2w)(5 + -1w) = 0Subproblem 1
Set the factor '(5 + -2w)' equal to zero and attempt to solve: Simplifying 5 + -2w = 0 Solving 5 + -2w = 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 + -2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2w = 0 + -5 -2w = 0 + -5 Combine like terms: 0 + -5 = -5 -2w = -5 Divide each side by '-2'. w = 2.5 Simplifying w = 2.5Subproblem 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 = {2.5, 5}
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