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Simplifying -4b2 + 16b + 56 = -9 Reorder the terms: 56 + 16b + -4b2 = -9 Solving 56 + 16b + -4b2 = -9 Solving for variable 'b'. Reorder the terms: 56 + 9 + 16b + -4b2 = -9 + 9 Combine like terms: 56 + 9 = 65 65 + 16b + -4b2 = -9 + 9 Combine like terms: -9 + 9 = 0 65 + 16b + -4b2 = 0 Factor a trinomial. (13 + -2b)(5 + 2b) = 0Subproblem 1
Set the factor '(13 + -2b)' equal to zero and attempt to solve: Simplifying 13 + -2b = 0 Solving 13 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -2b = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -2b = 0 + -13 -2b = 0 + -13 Combine like terms: 0 + -13 = -13 -2b = -13 Divide each side by '-2'. b = 6.5 Simplifying b = 6.5Subproblem 2
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 = -2.5Solution
b = {6.5, -2.5}
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