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Simplifying 12w = 4w2 + 9 Reorder the terms: 12w = 9 + 4w2 Solving 12w = 9 + 4w2 Solving for variable 'w'. Reorder the terms: -9 + 12w + -4w2 = 9 + 4w2 + -9 + -4w2 Reorder the terms: -9 + 12w + -4w2 = 9 + -9 + 4w2 + -4w2 Combine like terms: 9 + -9 = 0 -9 + 12w + -4w2 = 0 + 4w2 + -4w2 -9 + 12w + -4w2 = 4w2 + -4w2 Combine like terms: 4w2 + -4w2 = 0 -9 + 12w + -4w2 = 0 Factor a trinomial. (-3 + 2w)(3 + -2w) = 0Subproblem 1
Set the factor '(-3 + 2w)' equal to zero and attempt to solve: Simplifying -3 + 2w = 0 Solving -3 + 2w = 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 + 2w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2w = 0 + 3 2w = 0 + 3 Combine like terms: 0 + 3 = 3 2w = 3 Divide each side by '2'. w = 1.5 Simplifying w = 1.5Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 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 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5Solution
w = {1.5, 1.5}
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