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Simplifying w(4w + 1) = 3 Reorder the terms: w(1 + 4w) = 3 (1 * w + 4w * w) = 3 (1w + 4w2) = 3 Solving 1w + 4w2 = 3 Solving for variable 'w'. Reorder the terms: -3 + 1w + 4w2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 1w + 4w2 = 0 Factor a trinomial. (-1 + -1w)(3 + -4w) = 0Subproblem 1
Set the factor '(-1 + -1w)' equal to zero and attempt to solve: Simplifying -1 + -1w = 0 Solving -1 + -1w = 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 + -1w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1w = 0 + 1 -1w = 0 + 1 Combine like terms: 0 + 1 = 1 -1w = 1 Divide each side by '-1'. w = -1 Simplifying w = -1Subproblem 2
Set the factor '(3 + -4w)' equal to zero and attempt to solve: Simplifying 3 + -4w = 0 Solving 3 + -4w = 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 + -4w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4w = 0 + -3 -4w = 0 + -3 Combine like terms: 0 + -3 = -3 -4w = -3 Divide each side by '-4'. w = 0.75 Simplifying w = 0.75Solution
w = {-1, 0.75}
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