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Simplifying (5 + w)(5w + -7) = 0 Reorder the terms: (5 + w)(-7 + 5w) = 0 Multiply (5 + w) * (-7 + 5w) (5(-7 + 5w) + w(-7 + 5w)) = 0 ((-7 * 5 + 5w * 5) + w(-7 + 5w)) = 0 ((-35 + 25w) + w(-7 + 5w)) = 0 (-35 + 25w + (-7 * w + 5w * w)) = 0 (-35 + 25w + (-7w + 5w2)) = 0 Combine like terms: 25w + -7w = 18w (-35 + 18w + 5w2) = 0 Solving -35 + 18w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (-5 + -1w)(7 + -5w) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(7 + -5w)' equal to zero and attempt to solve: Simplifying 7 + -5w = 0 Solving 7 + -5w = 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 + -5w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5w = 0 + -7 -5w = 0 + -7 Combine like terms: 0 + -7 = -7 -5w = -7 Divide each side by '-5'. w = 1.4 Simplifying w = 1.4Solution
w = {-5, 1.4}
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