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Simplifying (10 + -5) + (30 + -2w + 4)(5w + -3) + 20 = 25 Combine like terms: 10 + -5 = 5 (5) + (30 + -2w + 4)(5w + -3) + 20 = 25 5 + (30 + -2w + 4)(5w + -3) + 20 = 25 Reorder the terms: 5 + (30 + 4 + -2w)(5w + -3) + 20 = 25 Combine like terms: 30 + 4 = 34 5 + (34 + -2w)(5w + -3) + 20 = 25 Reorder the terms: 5 + (34 + -2w)(-3 + 5w) + 20 = 25 Multiply (34 + -2w) * (-3 + 5w) 5 + (34(-3 + 5w) + -2w * (-3 + 5w)) + 20 = 25 5 + ((-3 * 34 + 5w * 34) + -2w * (-3 + 5w)) + 20 = 25 5 + ((-102 + 170w) + -2w * (-3 + 5w)) + 20 = 25 5 + (-102 + 170w + (-3 * -2w + 5w * -2w)) + 20 = 25 5 + (-102 + 170w + (6w + -10w2)) + 20 = 25 Combine like terms: 170w + 6w = 176w 5 + (-102 + 176w + -10w2) + 20 = 25 Reorder the terms: 5 + -102 + 20 + 176w + -10w2 = 25 Combine like terms: 5 + -102 = -97 -97 + 20 + 176w + -10w2 = 25 Combine like terms: -97 + 20 = -77 -77 + 176w + -10w2 = 25 Solving -77 + 176w + -10w2 = 25 Solving for variable 'w'. Reorder the terms: -77 + -25 + 176w + -10w2 = 25 + -25 Combine like terms: -77 + -25 = -102 -102 + 176w + -10w2 = 25 + -25 Combine like terms: 25 + -25 = 0 -102 + 176w + -10w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-51 + 88w + -5w2) = 0 Factor a trinomial. 2((-17 + w)(3 + -5w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + w)' equal to zero and attempt to solve: Simplifying -17 + w = 0 Solving -17 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + w = 0 + 17 Combine like terms: -17 + 17 = 0 0 + w = 0 + 17 w = 0 + 17 Combine like terms: 0 + 17 = 17 w = 17 Simplifying w = 17Subproblem 2
Set the factor '(3 + -5w)' equal to zero and attempt to solve: Simplifying 3 + -5w = 0 Solving 3 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5w = 0 + -3 -5w = 0 + -3 Combine like terms: 0 + -3 = -3 -5w = -3 Divide each side by '-5'. w = 0.6 Simplifying w = 0.6Solution
w = {17, 0.6}
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