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Simplifying (3w + 11) * w = 70 Reorder the terms: (11 + 3w) * w = 70 Reorder the terms for easier multiplication: w(11 + 3w) = 70 (11 * w + 3w * w) = 70 (11w + 3w2) = 70 Solving 11w + 3w2 = 70 Solving for variable 'w'. Reorder the terms: -70 + 11w + 3w2 = 70 + -70 Combine like terms: 70 + -70 = 0 -70 + 11w + 3w2 = 0 Factor a trinomial. (-7 + -1w)(10 + -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 '(10 + -3w)' equal to zero and attempt to solve: Simplifying 10 + -3w = 0 Solving 10 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3w = 0 + -10 -3w = 0 + -10 Combine like terms: 0 + -10 = -10 -3w = -10 Divide each side by '-3'. w = 3.333333333 Simplifying w = 3.333333333Solution
w = {-7, 3.333333333}
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