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Simplifying 2w2 + 11w + 19 = w2 + 10w + 25 Reorder the terms: 19 + 11w + 2w2 = w2 + 10w + 25 Reorder the terms: 19 + 11w + 2w2 = 25 + 10w + w2 Solving 19 + 11w + 2w2 = 25 + 10w + w2 Solving for variable 'w'. Reorder the terms: 19 + -25 + 11w + -10w + 2w2 + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2 Combine like terms: 19 + -25 = -6 -6 + 11w + -10w + 2w2 + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2 Combine like terms: 11w + -10w = 1w -6 + 1w + 2w2 + -1w2 = 25 + 10w + w2 + -25 + -10w + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 -6 + 1w + 1w2 = 25 + 10w + w2 + -25 + -10w + -1w2 Reorder the terms: -6 + 1w + 1w2 = 25 + -25 + 10w + -10w + w2 + -1w2 Combine like terms: 25 + -25 = 0 -6 + 1w + 1w2 = 0 + 10w + -10w + w2 + -1w2 -6 + 1w + 1w2 = 10w + -10w + w2 + -1w2 Combine like terms: 10w + -10w = 0 -6 + 1w + 1w2 = 0 + w2 + -1w2 -6 + 1w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -6 + 1w + 1w2 = 0 Factor a trinomial. (-3 + -1w)(2 + -1w) = 0Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 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 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 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 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Solution
w = {-3, 2}
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