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Simplifying (w + -4) = 2w2 + -7w + 4 Reorder the terms: (-4 + w) = 2w2 + -7w + 4 Remove parenthesis around (-4 + w) -4 + w = 2w2 + -7w + 4 Reorder the terms: -4 + w = 4 + -7w + 2w2 Solving -4 + w = 4 + -7w + 2w2 Solving for variable 'w'. Reorder the terms: -4 + -4 + w + 7w + -2w2 = 4 + -7w + 2w2 + -4 + 7w + -2w2 Combine like terms: -4 + -4 = -8 -8 + w + 7w + -2w2 = 4 + -7w + 2w2 + -4 + 7w + -2w2 Combine like terms: w + 7w = 8w -8 + 8w + -2w2 = 4 + -7w + 2w2 + -4 + 7w + -2w2 Reorder the terms: -8 + 8w + -2w2 = 4 + -4 + -7w + 7w + 2w2 + -2w2 Combine like terms: 4 + -4 = 0 -8 + 8w + -2w2 = 0 + -7w + 7w + 2w2 + -2w2 -8 + 8w + -2w2 = -7w + 7w + 2w2 + -2w2 Combine like terms: -7w + 7w = 0 -8 + 8w + -2w2 = 0 + 2w2 + -2w2 -8 + 8w + -2w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -8 + 8w + -2w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 4w + -1w2) = 0 Factor a trinomial. 2((-2 + w)(2 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + w)' equal to zero and attempt to solve: Simplifying -2 + w = 0 Solving -2 + w = 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 + w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + w = 0 + 2 w = 0 + 2 Combine like terms: 0 + 2 = 2 w = 2 Simplifying w = 2Subproblem 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 = {2, 2}
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