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Simplifying 24b2 + -6b = 63 Reorder the terms: -6b + 24b2 = 63 Solving -6b + 24b2 = 63 Solving for variable 'b'. Reorder the terms: -63 + -6b + 24b2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + -6b + 24b2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-21 + -2b + 8b2) = 0 Factor a trinomial. 3((-3 + -2b)(7 + -4b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -2b)' equal to zero and attempt to solve: Simplifying -3 + -2b = 0 Solving -3 + -2b = 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 + -2b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2b = 0 + 3 -2b = 0 + 3 Combine like terms: 0 + 3 = 3 -2b = 3 Divide each side by '-2'. b = -1.5 Simplifying b = -1.5Subproblem 2
Set the factor '(7 + -4b)' equal to zero and attempt to solve: Simplifying 7 + -4b = 0 Solving 7 + -4b = 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 + -4b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4b = 0 + -7 -4b = 0 + -7 Combine like terms: 0 + -7 = -7 -4b = -7 Divide each side by '-4'. b = 1.75 Simplifying b = 1.75Solution
b = {-1.5, 1.75}
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