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Simplifying 30w2 + 115w + 100 = 0 Reorder the terms: 100 + 115w + 30w2 = 0 Solving 100 + 115w + 30w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5'. 5(20 + 23w + 6w2) = 0 Factor a trinomial. 5((5 + 2w)(4 + 3w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + 2w)' equal to zero and attempt to solve: Simplifying 5 + 2w = 0 Solving 5 + 2w = 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 + 2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2w = 0 + -5 2w = 0 + -5 Combine like terms: 0 + -5 = -5 2w = -5 Divide each side by '2'. w = -2.5 Simplifying w = -2.5Subproblem 2
Set the factor '(4 + 3w)' equal to zero and attempt to solve: Simplifying 4 + 3w = 0 Solving 4 + 3w = 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 + 3w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3w = 0 + -4 3w = 0 + -4 Combine like terms: 0 + -4 = -4 3w = -4 Divide each side by '3'. w = -1.333333333 Simplifying w = -1.333333333Solution
w = {-2.5, -1.333333333}
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