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Simplifying 4b2 + 16b + 8 = -7 Reorder the terms: 8 + 16b + 4b2 = -7 Solving 8 + 16b + 4b2 = -7 Solving for variable 'b'. Reorder the terms: 8 + 7 + 16b + 4b2 = -7 + 7 Combine like terms: 8 + 7 = 15 15 + 16b + 4b2 = -7 + 7 Combine like terms: -7 + 7 = 0 15 + 16b + 4b2 = 0 Factor a trinomial. (5 + 2b)(3 + 2b) = 0Subproblem 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 '(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 = -1.5Solution
b = {-2.5, -1.5}
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