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Simplifying 2w2 + 16w + 25 + -1w2 + -14w + -49 = 0 Reorder the terms: 25 + -49 + 16w + -14w + 2w2 + -1w2 = 0 Combine like terms: 25 + -49 = -24 -24 + 16w + -14w + 2w2 + -1w2 = 0 Combine like terms: 16w + -14w = 2w -24 + 2w + 2w2 + -1w2 = 0 Combine like terms: 2w2 + -1w2 = 1w2 -24 + 2w + 1w2 = 0 Solving -24 + 2w + 1w2 = 0 Solving for variable 'w'. Factor a trinomial. (-6 + -1w)(4 + -1w) = 0Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve: Simplifying -6 + -1w = 0 Solving -6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1w = 0 + 6 -1w = 0 + 6 Combine like terms: 0 + 6 = 6 -1w = 6 Divide each side by '-1'. w = -6 Simplifying w = -6Subproblem 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 = {-6, 4}
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