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Simplifying 10 = 6w2 + -7w Reorder the terms: 10 = -7w + 6w2 Solving 10 = -7w + 6w2 Solving for variable 'w'. Reorder the terms: 10 + 7w + -6w2 = -7w + 7w + 6w2 + -6w2 Combine like terms: -7w + 7w = 0 10 + 7w + -6w2 = 0 + 6w2 + -6w2 10 + 7w + -6w2 = 6w2 + -6w2 Combine like terms: 6w2 + -6w2 = 0 10 + 7w + -6w2 = 0 Factor a trinomial. (2 + -1w)(5 + 6w) = 0Subproblem 1
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 = 2Subproblem 2
Set the factor '(5 + 6w)' equal to zero and attempt to solve: Simplifying 5 + 6w = 0 Solving 5 + 6w = 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 + 6w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6w = 0 + -5 6w = 0 + -5 Combine like terms: 0 + -5 = -5 6w = -5 Divide each side by '6'. w = -0.8333333333 Simplifying w = -0.8333333333Solution
w = {2, -0.8333333333}
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