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Simplifying 176 = 2w2 + 6w Reorder the terms: 176 = 6w + 2w2 Solving 176 = 6w + 2w2 Solving for variable 'w'. Reorder the terms: 176 + -6w + -2w2 = 6w + -6w + 2w2 + -2w2 Combine like terms: 6w + -6w = 0 176 + -6w + -2w2 = 0 + 2w2 + -2w2 176 + -6w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 176 + -6w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(88 + -3w + -1w2) = 0 Factor a trinomial. 2((8 + -1w)(11 + w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Subproblem 2
Set the factor '(11 + w)' equal to zero and attempt to solve: Simplifying 11 + w = 0 Solving 11 + w = 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 + w = 0 + -11 Combine like terms: 11 + -11 = 0 0 + w = 0 + -11 w = 0 + -11 Combine like terms: 0 + -11 = -11 w = -11 Simplifying w = -11Solution
w = {8, -11}
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