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Simplifying 2w2 + 6w + 44 = w2 + 36 Reorder the terms: 44 + 6w + 2w2 = w2 + 36 Reorder the terms: 44 + 6w + 2w2 = 36 + w2 Solving 44 + 6w + 2w2 = 36 + w2 Solving for variable 'w'. Reorder the terms: 44 + -36 + 6w + 2w2 + -1w2 = 36 + w2 + -36 + -1w2 Combine like terms: 44 + -36 = 8 8 + 6w + 2w2 + -1w2 = 36 + w2 + -36 + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 8 + 6w + 1w2 = 36 + w2 + -36 + -1w2 Reorder the terms: 8 + 6w + 1w2 = 36 + -36 + w2 + -1w2 Combine like terms: 36 + -36 = 0 8 + 6w + 1w2 = 0 + w2 + -1w2 8 + 6w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 8 + 6w + 1w2 = 0 Factor a trinomial. (4 + w)(2 + w) = 0Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 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 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2Solution
w = {-4, -2}
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