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Simplifying 2w2 + -12w + 16 = 70 Reorder the terms: 16 + -12w + 2w2 = 70 Solving 16 + -12w + 2w2 = 70 Solving for variable 'w'. Reorder the terms: 16 + -70 + -12w + 2w2 = 70 + -70 Combine like terms: 16 + -70 = -54 -54 + -12w + 2w2 = 70 + -70 Combine like terms: 70 + -70 = 0 -54 + -12w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -6w + w2) = 0 Factor a trinomial. 2((-3 + -1w)(9 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 2
Set the factor '(9 + -1w)' equal to zero and attempt to solve: Simplifying 9 + -1w = 0 Solving 9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1w = 0 + -9 -1w = 0 + -9 Combine like terms: 0 + -9 = -9 -1w = -9 Divide each side by '-1'. w = 9 Simplifying w = 9Solution
w = {-3, 9}
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