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Simplifying 2w2 + 52w + -112 = 0 Reorder the terms: -112 + 52w + 2w2 = 0 Solving -112 + 52w + 2w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-56 + 26w + w2) = 0 Factor a trinomial. 2((-28 + -1w)(2 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + -1w)' equal to zero and attempt to solve: Simplifying -28 + -1w = 0 Solving -28 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + -1w = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -1w = 0 + 28 -1w = 0 + 28 Combine like terms: 0 + 28 = 28 -1w = 28 Divide each side by '-1'. w = -28 Simplifying w = -28Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Solution
w = {-28, 2}
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