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Simplifying 0 = 2w2 + 8w + -2170 Reorder the terms: 0 = -2170 + 8w + 2w2 Solving 0 = -2170 + 8w + 2w2 Solving for variable 'w'. Combine like terms: 0 + 2170 = 2170 2170 + -8w + -2w2 = -2170 + 8w + 2w2 + 2170 + -8w + -2w2 Reorder the terms: 2170 + -8w + -2w2 = -2170 + 2170 + 8w + -8w + 2w2 + -2w2 Combine like terms: -2170 + 2170 = 0 2170 + -8w + -2w2 = 0 + 8w + -8w + 2w2 + -2w2 2170 + -8w + -2w2 = 8w + -8w + 2w2 + -2w2 Combine like terms: 8w + -8w = 0 2170 + -8w + -2w2 = 0 + 2w2 + -2w2 2170 + -8w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 2170 + -8w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1085 + -4w + -1w2) = 0 Factor a trinomial. 2((31 + -1w)(35 + w)) = 0 Ignore the factor 2.Subproblem 1
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 = 31Subproblem 2
Set the factor '(35 + w)' equal to zero and attempt to solve: Simplifying 35 + w = 0 Solving 35 + w = 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 + w = 0 + -35 Combine like terms: 35 + -35 = 0 0 + w = 0 + -35 w = 0 + -35 Combine like terms: 0 + -35 = -35 w = -35 Simplifying w = -35Solution
w = {31, -35}
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