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Simplifying (2w + 17)(1w + -7) = 0 Reorder the terms: (17 + 2w)(1w + -7) = 0 Reorder the terms: (17 + 2w)(-7 + 1w) = 0 Multiply (17 + 2w) * (-7 + 1w) (17(-7 + 1w) + 2w * (-7 + 1w)) = 0 ((-7 * 17 + 1w * 17) + 2w * (-7 + 1w)) = 0 ((-119 + 17w) + 2w * (-7 + 1w)) = 0 (-119 + 17w + (-7 * 2w + 1w * 2w)) = 0 (-119 + 17w + (-14w + 2w2)) = 0 Combine like terms: 17w + -14w = 3w (-119 + 3w + 2w2) = 0 Solving -119 + 3w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-17 + -2w)(7 + -1w) = 0Subproblem 1
Set the factor '(-17 + -2w)' equal to zero and attempt to solve: Simplifying -17 + -2w = 0 Solving -17 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -2w = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -2w = 0 + 17 -2w = 0 + 17 Combine like terms: 0 + 17 = 17 -2w = 17 Divide each side by '-2'. w = -8.5 Simplifying w = -8.5Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Solution
w = {-8.5, 7}
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