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Simplifying (7w2 + -7w + -8) + -1(5w2 + 2w + -3) = 0 Reorder the terms: (-8 + -7w + 7w2) + -1(5w2 + 2w + -3) = 0 Remove parenthesis around (-8 + -7w + 7w2) -8 + -7w + 7w2 + -1(5w2 + 2w + -3) = 0 Reorder the terms: -8 + -7w + 7w2 + -1(-3 + 2w + 5w2) = 0 -8 + -7w + 7w2 + (-3 * -1 + 2w * -1 + 5w2 * -1) = 0 -8 + -7w + 7w2 + (3 + -2w + -5w2) = 0 Reorder the terms: -8 + 3 + -7w + -2w + 7w2 + -5w2 = 0 Combine like terms: -8 + 3 = -5 -5 + -7w + -2w + 7w2 + -5w2 = 0 Combine like terms: -7w + -2w = -9w -5 + -9w + 7w2 + -5w2 = 0 Combine like terms: 7w2 + -5w2 = 2w2 -5 + -9w + 2w2 = 0 Solving -5 + -9w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-1 + -2w)(5 + -1w) = 0Subproblem 1
Set the factor '(-1 + -2w)' equal to zero and attempt to solve: Simplifying -1 + -2w = 0 Solving -1 + -2w = 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 + -2w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2w = 0 + 1 -2w = 0 + 1 Combine like terms: 0 + 1 = 1 -2w = 1 Divide each side by '-2'. w = -0.5 Simplifying w = -0.5Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Solution
w = {-0.5, 5}
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