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Simplifying 5w2 = 7w + 6 Reorder the terms: 5w2 = 6 + 7w Solving 5w2 = 6 + 7w Solving for variable 'w'. Reorder the terms: -6 + -7w + 5w2 = 6 + 7w + -6 + -7w Reorder the terms: -6 + -7w + 5w2 = 6 + -6 + 7w + -7w Combine like terms: 6 + -6 = 0 -6 + -7w + 5w2 = 0 + 7w + -7w -6 + -7w + 5w2 = 7w + -7w Combine like terms: 7w + -7w = 0 -6 + -7w + 5w2 = 0 Factor a trinomial. (-3 + -5w)(2 + -1w) = 0Subproblem 1
Set the factor '(-3 + -5w)' equal to zero and attempt to solve: Simplifying -3 + -5w = 0 Solving -3 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -5w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5w = 0 + 3 -5w = 0 + 3 Combine like terms: 0 + 3 = 3 -5w = 3 Divide each side by '-5'. w = -0.6 Simplifying w = -0.6Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Solution
w = {-0.6, 2}
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