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Simplifying (2w + -5) * w + -52 = 0 Reorder the terms: (-5 + 2w) * w + -52 = 0 Reorder the terms for easier multiplication: w(-5 + 2w) + -52 = 0 (-5 * w + 2w * w) + -52 = 0 (-5w + 2w2) + -52 = 0 Reorder the terms: -52 + -5w + 2w2 = 0 Solving -52 + -5w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-4 + -1w)(13 + -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 '(13 + -2w)' equal to zero and attempt to solve: Simplifying 13 + -2w = 0 Solving 13 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2w = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2w = 0 + -13 -2w = 0 + -13 Combine like terms: 0 + -13 = -13 -2w = -13 Divide each side by '-2'. w = 6.5 Simplifying w = 6.5Solution
w = {-4, 6.5}
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