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Simplifying (3w2 + -7w + 5) + (-4w2 + 2w + 1) = 0 Reorder the terms: (5 + -7w + 3w2) + (-4w2 + 2w + 1) = 0 Remove parenthesis around (5 + -7w + 3w2) 5 + -7w + 3w2 + (-4w2 + 2w + 1) = 0 Reorder the terms: 5 + -7w + 3w2 + (1 + 2w + -4w2) = 0 Remove parenthesis around (1 + 2w + -4w2) 5 + -7w + 3w2 + 1 + 2w + -4w2 = 0 Reorder the terms: 5 + 1 + -7w + 2w + 3w2 + -4w2 = 0 Combine like terms: 5 + 1 = 6 6 + -7w + 2w + 3w2 + -4w2 = 0 Combine like terms: -7w + 2w = -5w 6 + -5w + 3w2 + -4w2 = 0 Combine like terms: 3w2 + -4w2 = -1w2 6 + -5w + -1w2 = 0 Solving 6 + -5w + -1w2 = 0 Solving for variable 'w'. Factor a trinomial. (1 + -1w)(6 + w) = 0Subproblem 1
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Subproblem 2
Set the factor '(6 + w)' equal to zero and attempt to solve: Simplifying 6 + w = 0 Solving 6 + w = 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 + w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + w = 0 + -6 w = 0 + -6 Combine like terms: 0 + -6 = -6 w = -6 Simplifying w = -6Solution
w = {1, -6}
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