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Simplifying (1 + -1w)(2w + -5) = 0 Reorder the terms: (1 + -1w)(-5 + 2w) = 0 Multiply (1 + -1w) * (-5 + 2w) (1(-5 + 2w) + -1w * (-5 + 2w)) = 0 ((-5 * 1 + 2w * 1) + -1w * (-5 + 2w)) = 0 ((-5 + 2w) + -1w * (-5 + 2w)) = 0 (-5 + 2w + (-5 * -1w + 2w * -1w)) = 0 (-5 + 2w + (5w + -2w2)) = 0 Combine like terms: 2w + 5w = 7w (-5 + 7w + -2w2) = 0 Solving -5 + 7w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-5 + 2w)(1 + -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 '(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 = {2.5, 1}
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