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Simplifying w(4w + 4) = 3 Reorder the terms: w(4 + 4w) = 3 (4 * w + 4w * w) = 3 (4w + 4w2) = 3 Solving 4w + 4w2 = 3 Solving for variable 'w'. Reorder the terms: -3 + 4w + 4w2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 4w + 4w2 = 0 Factor a trinomial. (-3 + -2w)(1 + -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 '(1 + -2w)' equal to zero and attempt to solve: Simplifying 1 + -2w = 0 Solving 1 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2w = 0 + -1 -2w = 0 + -1 Combine like terms: 0 + -1 = -1 -2w = -1 Divide each side by '-2'. w = 0.5 Simplifying w = 0.5Solution
w = {-1.5, 0.5}
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