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Simplifying 7b2 + -14b + -66 = -10 Reorder the terms: -66 + -14b + 7b2 = -10 Solving -66 + -14b + 7b2 = -10 Solving for variable 'b'. Reorder the terms: -66 + 10 + -14b + 7b2 = -10 + 10 Combine like terms: -66 + 10 = -56 -56 + -14b + 7b2 = -10 + 10 Combine like terms: -10 + 10 = 0 -56 + -14b + 7b2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-8 + -2b + b2) = 0 Factor a trinomial. 7((-2 + -1b)(4 + -1b)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-2 + -1b)' equal to zero and attempt to solve: Simplifying -2 + -1b = 0 Solving -2 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1b = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1b = 0 + 2 -1b = 0 + 2 Combine like terms: 0 + 2 = 2 -1b = 2 Divide each side by '-1'. b = -2 Simplifying b = -2Subproblem 2
Set the factor '(4 + -1b)' equal to zero and attempt to solve: Simplifying 4 + -1b = 0 Solving 4 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1b = 0 + -4 -1b = 0 + -4 Combine like terms: 0 + -4 = -4 -1b = -4 Divide each side by '-1'. b = 4 Simplifying b = 4Solution
b = {-2, 4}
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