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Simplifying 7b2 + 12b + -5 = -2b2 Reorder the terms: -5 + 12b + 7b2 = -2b2 Solving -5 + 12b + 7b2 = -2b2 Solving for variable 'b'. Combine like terms: 7b2 + 2b2 = 9b2 -5 + 12b + 9b2 = -2b2 + 2b2 Combine like terms: -2b2 + 2b2 = 0 -5 + 12b + 9b2 = 0 Factor a trinomial. (-5 + -3b)(1 + -3b) = 0Subproblem 1
Set the factor '(-5 + -3b)' equal to zero and attempt to solve: Simplifying -5 + -3b = 0 Solving -5 + -3b = 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 + -3b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3b = 0 + 5 -3b = 0 + 5 Combine like terms: 0 + 5 = 5 -3b = 5 Divide each side by '-3'. b = -1.666666667 Simplifying b = -1.666666667Subproblem 2
Set the factor '(1 + -3b)' equal to zero and attempt to solve: Simplifying 1 + -3b = 0 Solving 1 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3b = 0 + -1 -3b = 0 + -1 Combine like terms: 0 + -1 = -1 -3b = -1 Divide each side by '-3'. b = 0.3333333333 Simplifying b = 0.3333333333Solution
b = {-1.666666667, 0.3333333333}
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