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Simplifying w(2w + 1) = 36 Reorder the terms: w(1 + 2w) = 36 (1 * w + 2w * w) = 36 (1w + 2w2) = 36 Solving 1w + 2w2 = 36 Solving for variable 'w'. Reorder the terms: -36 + 1w + 2w2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + 1w + 2w2 = 0 Factor a trinomial. (-9 + -2w)(4 + -1w) = 0Subproblem 1
Set the factor '(-9 + -2w)' equal to zero and attempt to solve: Simplifying -9 + -2w = 0 Solving -9 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2w = 0 + 9 -2w = 0 + 9 Combine like terms: 0 + 9 = 9 -2w = 9 Divide each side by '-2'. w = -4.5 Simplifying w = -4.5Subproblem 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 = {-4.5, 4}
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