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Simplifying 12b2 + 102b + 28 = -2b2 Reorder the terms: 28 + 102b + 12b2 = -2b2 Solving 28 + 102b + 12b2 = -2b2 Solving for variable 'b'. Combine like terms: 12b2 + 2b2 = 14b2 28 + 102b + 14b2 = -2b2 + 2b2 Combine like terms: -2b2 + 2b2 = 0 28 + 102b + 14b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 51b + 7b2) = 0 Factor a trinomial. 2((7 + b)(2 + 7b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + b)' equal to zero and attempt to solve: Simplifying 7 + b = 0 Solving 7 + b = 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 + b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + b = 0 + -7 b = 0 + -7 Combine like terms: 0 + -7 = -7 b = -7 Simplifying b = -7Subproblem 2
Set the factor '(2 + 7b)' equal to zero and attempt to solve: Simplifying 2 + 7b = 0 Solving 2 + 7b = 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 + 7b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7b = 0 + -2 7b = 0 + -2 Combine like terms: 0 + -2 = -2 7b = -2 Divide each side by '7'. b = -0.2857142857 Simplifying b = -0.2857142857Solution
b = {-7, -0.2857142857}
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