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Simplifying 8b2 = 30 + 34b Solving 8b2 = 30 + 34b Solving for variable 'b'. Reorder the terms: -30 + -34b + 8b2 = 30 + 34b + -30 + -34b Reorder the terms: -30 + -34b + 8b2 = 30 + -30 + 34b + -34b Combine like terms: 30 + -30 = 0 -30 + -34b + 8b2 = 0 + 34b + -34b -30 + -34b + 8b2 = 34b + -34b Combine like terms: 34b + -34b = 0 -30 + -34b + 8b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -17b + 4b2) = 0 Factor a trinomial. 2((-3 + -4b)(5 + -1b)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.75Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve: Simplifying 5 + -1b = 0 Solving 5 + -1b = 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 + -1b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1b = 0 + -5 -1b = 0 + -5 Combine like terms: 0 + -5 = -5 -1b = -5 Divide each side by '-1'. b = 5 Simplifying b = 5Solution
b = {-0.75, 5}
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