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Simplifying 76w = 56 + -12w2 Solving 76w = 56 + -12w2 Solving for variable 'w'. Reorder the terms: -56 + 76w + 12w2 = 56 + -12w2 + -56 + 12w2 Reorder the terms: -56 + 76w + 12w2 = 56 + -56 + -12w2 + 12w2 Combine like terms: 56 + -56 = 0 -56 + 76w + 12w2 = 0 + -12w2 + 12w2 -56 + 76w + 12w2 = -12w2 + 12w2 Combine like terms: -12w2 + 12w2 = 0 -56 + 76w + 12w2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + 19w + 3w2) = 0 Factor a trinomial. 4((-7 + -1w)(2 + -3w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7Subproblem 2
Set the factor '(2 + -3w)' equal to zero and attempt to solve: Simplifying 2 + -3w = 0 Solving 2 + -3w = 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 + -3w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3w = 0 + -2 -3w = 0 + -2 Combine like terms: 0 + -2 = -2 -3w = -2 Divide each side by '-3'. w = 0.6666666667 Simplifying w = 0.6666666667Solution
w = {-7, 0.6666666667}
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