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Simplifying 8b2 = 192 + -40b Solving 8b2 = 192 + -40b Solving for variable 'b'. Reorder the terms: -192 + 40b + 8b2 = 192 + -40b + -192 + 40b Reorder the terms: -192 + 40b + 8b2 = 192 + -192 + -40b + 40b Combine like terms: 192 + -192 = 0 -192 + 40b + 8b2 = 0 + -40b + 40b -192 + 40b + 8b2 = -40b + 40b Combine like terms: -40b + 40b = 0 -192 + 40b + 8b2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-24 + 5b + b2) = 0 Factor a trinomial. 8((-8 + -1b)(3 + -1b)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-8 + -1b)' equal to zero and attempt to solve: Simplifying -8 + -1b = 0 Solving -8 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1b = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1b = 0 + 8 -1b = 0 + 8 Combine like terms: 0 + 8 = 8 -1b = 8 Divide each side by '-1'. b = -8 Simplifying b = -8Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve: Simplifying 3 + -1b = 0 Solving 3 + -1b = 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 + -1b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1b = 0 + -3 -1b = 0 + -3 Combine like terms: 0 + -3 = -3 -1b = -3 Divide each side by '-1'. b = 3 Simplifying b = 3Solution
b = {-8, 3}
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