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Simplifying 8w2 + 28w + 12 = 3772 Reorder the terms: 12 + 28w + 8w2 = 3772 Solving 12 + 28w + 8w2 = 3772 Solving for variable 'w'. Reorder the terms: 12 + -3772 + 28w + 8w2 = 3772 + -3772 Combine like terms: 12 + -3772 = -3760 -3760 + 28w + 8w2 = 3772 + -3772 Combine like terms: 3772 + -3772 = 0 -3760 + 28w + 8w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-940 + 7w + 2w2) = 0 Factor a trinomial. 4((-47 + -2w)(20 + -1w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-47 + -2w)' equal to zero and attempt to solve: Simplifying -47 + -2w = 0 Solving -47 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '47' to each side of the equation. -47 + 47 + -2w = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -2w = 0 + 47 -2w = 0 + 47 Combine like terms: 0 + 47 = 47 -2w = 47 Divide each side by '-2'. w = -23.5 Simplifying w = -23.5Subproblem 2
Set the factor '(20 + -1w)' equal to zero and attempt to solve: Simplifying 20 + -1w = 0 Solving 20 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1w = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1w = 0 + -20 -1w = 0 + -20 Combine like terms: 0 + -20 = -20 -1w = -20 Divide each side by '-1'. w = 20 Simplifying w = 20Solution
w = {-23.5, 20}
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