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Simplifying 8b2 + 22b + -10 = 6b Reorder the terms: -10 + 22b + 8b2 = 6b Solving -10 + 22b + 8b2 = 6b Solving for variable 'b'. Reorder the terms: -10 + 22b + -6b + 8b2 = 6b + -6b Combine like terms: 22b + -6b = 16b -10 + 16b + 8b2 = 6b + -6b Combine like terms: 6b + -6b = 0 -10 + 16b + 8b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 8b + 4b2) = 0 Factor a trinomial. 2((-5 + -2b)(1 + -2b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -2b)' equal to zero and attempt to solve: Simplifying -5 + -2b = 0 Solving -5 + -2b = 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 + -2b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2b = 0 + 5 -2b = 0 + 5 Combine like terms: 0 + 5 = 5 -2b = 5 Divide each side by '-2'. b = -2.5 Simplifying b = -2.5Subproblem 2
Set the factor '(1 + -2b)' equal to zero and attempt to solve: Simplifying 1 + -2b = 0 Solving 1 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2b = 0 + -1 -2b = 0 + -1 Combine like terms: 0 + -1 = -1 -2b = -1 Divide each side by '-2'. b = 0.5 Simplifying b = 0.5Solution
b = {-2.5, 0.5}
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