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Simplifying 32w2 + 20w + -3 = 0 Reorder the terms: -3 + 20w + 32w2 = 0 Solving -3 + 20w + 32w2 = 0 Solving for variable 'w'. Factor a trinomial. (-3 + -4w)(1 + -8w) = 0Subproblem 1
Set the factor '(-3 + -4w)' equal to zero and attempt to solve: Simplifying -3 + -4w = 0 Solving -3 + -4w = 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 + -4w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4w = 0 + 3 -4w = 0 + 3 Combine like terms: 0 + 3 = 3 -4w = 3 Divide each side by '-4'. w = -0.75 Simplifying w = -0.75Subproblem 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 = {-0.75, 0.125}
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