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Simplifying 77 = (3w + -10) * w Reorder the terms: 77 = (-10 + 3w) * w Reorder the terms for easier multiplication: 77 = w(-10 + 3w) 77 = (-10 * w + 3w * w) 77 = (-10w + 3w2) Solving 77 = -10w + 3w2 Solving for variable 'w'. Reorder the terms: 77 + 10w + -3w2 = -10w + 10w + 3w2 + -3w2 Combine like terms: -10w + 10w = 0 77 + 10w + -3w2 = 0 + 3w2 + -3w2 77 + 10w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 77 + 10w + -3w2 = 0 Factor a trinomial. (7 + -1w)(11 + 3w) = 0Subproblem 1
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 = 7Subproblem 2
Set the factor '(11 + 3w)' equal to zero and attempt to solve: Simplifying 11 + 3w = 0 Solving 11 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 3w = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 3w = 0 + -11 3w = 0 + -11 Combine like terms: 0 + -11 = -11 3w = -11 Divide each side by '3'. w = -3.666666667 Simplifying w = -3.666666667Solution
w = {7, -3.666666667}
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