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Simplifying 24b2 + -392 = -112b Reorder the terms: -392 + 24b2 = -112b Solving -392 + 24b2 = -112b Solving for variable 'b'. Reorder the terms: -392 + 112b + 24b2 = -112b + 112b Combine like terms: -112b + 112b = 0 -392 + 112b + 24b2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-49 + 14b + 3b2) = 0 Factor a trinomial. 8((-7 + -1b)(7 + -3b)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-7 + -1b)' equal to zero and attempt to solve: Simplifying -7 + -1b = 0 Solving -7 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1b = 0 + 7 -1b = 0 + 7 Combine like terms: 0 + 7 = 7 -1b = 7 Divide each side by '-1'. b = -7 Simplifying b = -7Subproblem 2
Set the factor '(7 + -3b)' equal to zero and attempt to solve: Simplifying 7 + -3b = 0 Solving 7 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3b = 0 + -7 -3b = 0 + -7 Combine like terms: 0 + -7 = -7 -3b = -7 Divide each side by '-3'. b = 2.333333333 Simplifying b = 2.333333333Solution
b = {-7, 2.333333333}
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