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Simplifying (7w2 + -2w + 3) + (7w2 + -8w + 4) + -1(-1w2 + 4w + 7) = 0 Reorder the terms: (3 + -2w + 7w2) + (7w2 + -8w + 4) + -1(-1w2 + 4w + 7) = 0 Remove parenthesis around (3 + -2w + 7w2) 3 + -2w + 7w2 + (7w2 + -8w + 4) + -1(-1w2 + 4w + 7) = 0 Reorder the terms: 3 + -2w + 7w2 + (4 + -8w + 7w2) + -1(-1w2 + 4w + 7) = 0 Remove parenthesis around (4 + -8w + 7w2) 3 + -2w + 7w2 + 4 + -8w + 7w2 + -1(-1w2 + 4w + 7) = 0 Reorder the terms: 3 + -2w + 7w2 + 4 + -8w + 7w2 + -1(7 + 4w + -1w2) = 0 3 + -2w + 7w2 + 4 + -8w + 7w2 + (7 * -1 + 4w * -1 + -1w2 * -1) = 0 3 + -2w + 7w2 + 4 + -8w + 7w2 + (-7 + -4w + 1w2) = 0 Reorder the terms: 3 + 4 + -7 + -2w + -8w + -4w + 7w2 + 7w2 + 1w2 = 0 Combine like terms: 3 + 4 = 7 7 + -7 + -2w + -8w + -4w + 7w2 + 7w2 + 1w2 = 0 Combine like terms: 7 + -7 = 0 0 + -2w + -8w + -4w + 7w2 + 7w2 + 1w2 = 0 -2w + -8w + -4w + 7w2 + 7w2 + 1w2 = 0 Combine like terms: -2w + -8w = -10w -10w + -4w + 7w2 + 7w2 + 1w2 = 0 Combine like terms: -10w + -4w = -14w -14w + 7w2 + 7w2 + 1w2 = 0 Combine like terms: 7w2 + 7w2 = 14w2 -14w + 14w2 + 1w2 = 0 Combine like terms: 14w2 + 1w2 = 15w2 -14w + 15w2 = 0 Solving -14w + 15w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w'. w(-14 + 15w) = 0Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(-14 + 15w)' equal to zero and attempt to solve: Simplifying -14 + 15w = 0 Solving -14 + 15w = 0 Move all terms containing w to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + 15w = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 15w = 0 + 14 15w = 0 + 14 Combine like terms: 0 + 14 = 14 15w = 14 Divide each side by '15'. w = 0.9333333333 Simplifying w = 0.9333333333Solution
w = {0, 0.9333333333}
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