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Simplifying 2w2 + 8w = 2170 Reorder the terms: 8w + 2w2 = 2170 Solving 8w + 2w2 = 2170 Solving for variable 'w'. Reorder the terms: -2170 + 8w + 2w2 = 2170 + -2170 Combine like terms: 2170 + -2170 = 0 -2170 + 8w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1085 + 4w + w2) = 0 Factor a trinomial. 2((-35 + -1w)(31 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + -1w)' equal to zero and attempt to solve: Simplifying -35 + -1w = 0 Solving -35 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + -1w = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -1w = 0 + 35 -1w = 0 + 35 Combine like terms: 0 + 35 = 35 -1w = 35 Divide each side by '-1'. w = -35 Simplifying w = -35Subproblem 2
Set the factor '(31 + -1w)' equal to zero and attempt to solve: Simplifying 31 + -1w = 0 Solving 31 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + -1w = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -1w = 0 + -31 -1w = 0 + -31 Combine like terms: 0 + -31 = -31 -1w = -31 Divide each side by '-1'. w = 31 Simplifying w = 31Solution
w = {-35, 31}
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