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Simplifying w(2w + 1) = 28 Reorder the terms: w(1 + 2w) = 28 (1 * w + 2w * w) = 28 (1w + 2w2) = 28 Solving 1w + 2w2 = 28 Solving for variable 'w'. Reorder the terms: -28 + 1w + 2w2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 1w + 2w2 = 0 Factor a trinomial. (-4 + -1w)(7 + -2w) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(7 + -2w)' equal to zero and attempt to solve: Simplifying 7 + -2w = 0 Solving 7 + -2w = 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 + -2w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2w = 0 + -7 -2w = 0 + -7 Combine like terms: 0 + -7 = -7 -2w = -7 Divide each side by '-2'. w = 3.5 Simplifying w = 3.5Solution
w = {-4, 3.5}
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