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Simplifying 16w2 + 78w + -10 = 0 Reorder the terms: -10 + 78w + 16w2 = 0 Solving -10 + 78w + 16w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 39w + 8w2) = 0 Factor a trinomial. 2((-5 + -1w)(1 + -8w)) = 0 Ignore the factor 2.Subproblem 1
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 = -5Subproblem 2
Set the factor '(1 + -8w)' equal to zero and attempt to solve: Simplifying 1 + -8w = 0 Solving 1 + -8w = 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 + -8w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8w = 0 + -1 -8w = 0 + -1 Combine like terms: 0 + -1 = -1 -8w = -1 Divide each side by '-8'. w = 0.125 Simplifying w = 0.125Solution
w = {-5, 0.125}
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