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Simplifying -32b2 + 16b + 30 = 0 Reorder the terms: 30 + 16b + -32b2 = 0 Solving 30 + 16b + -32b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 8b + -16b2) = 0 Factor a trinomial. 2((5 + -4b)(3 + 4b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -4b)' equal to zero and attempt to solve: Simplifying 5 + -4b = 0 Solving 5 + -4b = 0 Move all terms containing b to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4b = 0 + -5 -4b = 0 + -5 Combine like terms: 0 + -5 = -5 -4b = -5 Divide each side by '-4'. b = 1.25 Simplifying b = 1.25Subproblem 2
Set the factor '(3 + 4b)' equal to zero and attempt to solve: Simplifying 3 + 4b = 0 Solving 3 + 4b = 0 Move all terms containing b to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4b = 0 + -3 4b = 0 + -3 Combine like terms: 0 + -3 = -3 4b = -3 Divide each side by '4'. b = -0.75 Simplifying b = -0.75Solution
b = {1.25, -0.75}
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