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Simplifying w2 + 5w + -32 + -2w + 4 = 0 Reorder the terms: -32 + 4 + 5w + -2w + w2 = 0 Combine like terms: -32 + 4 = -28 -28 + 5w + -2w + w2 = 0 Combine like terms: 5w + -2w = 3w -28 + 3w + w2 = 0 Solving -28 + 3w + w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + -1w)(4 + -1w) = 0Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 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 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7Subproblem 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 = {-7, 4}
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