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Simplifying 65 = (2w + -3) * w Reorder the terms: 65 = (-3 + 2w) * w Reorder the terms for easier multiplication: 65 = w(-3 + 2w) 65 = (-3 * w + 2w * w) 65 = (-3w + 2w2) Solving 65 = -3w + 2w2 Solving for variable 'w'. Reorder the terms: 65 + 3w + -2w2 = -3w + 3w + 2w2 + -2w2 Combine like terms: -3w + 3w = 0 65 + 3w + -2w2 = 0 + 2w2 + -2w2 65 + 3w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 65 + 3w + -2w2 = 0 Factor a trinomial. (13 + -2w)(5 + w) = 0Subproblem 1
Set the factor '(13 + -2w)' equal to zero and attempt to solve: Simplifying 13 + -2w = 0 Solving 13 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2w = 0 + -13 -2w = 0 + -13 Combine like terms: 0 + -13 = -13 -2w = -13 Divide each side by '-2'. w = 6.5 Simplifying w = 6.5Subproblem 2
Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 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 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Solution
w = {6.5, -5}
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