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Simplifying 4W2 + 12W + 9 = 121 Reorder the terms: 9 + 12W + 4W2 = 121 Solving 9 + 12W + 4W2 = 121 Solving for variable 'W'. Reorder the terms: 9 + -121 + 12W + 4W2 = 121 + -121 Combine like terms: 9 + -121 = -112 -112 + 12W + 4W2 = 121 + -121 Combine like terms: 121 + -121 = 0 -112 + 12W + 4W2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-28 + 3W + W2) = 0 Factor a trinomial. 4((-7 + -1W)(4 + -1W)) = 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 '(4 + -1W)' equal to zero and attempt to solve: Simplifying 4 + -1W = 0 Solving 4 + -1W = 0 Move all terms containing W to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1W = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1W = 0 + -4 -1W = 0 + -4 Combine like terms: 0 + -4 = -4 -1W = -4 Divide each side by '-1'. W = 4 Simplifying W = 4Solution
W = {-7, 4}
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