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Simplifying 10b2 + -19b = -7b + b2 + 96 Reorder the terms: -19b + 10b2 = -7b + b2 + 96 Reorder the terms: -19b + 10b2 = 96 + -7b + b2 Solving -19b + 10b2 = 96 + -7b + b2 Solving for variable 'b'. Reorder the terms: -96 + -19b + 7b + 10b2 + -1b2 = 96 + -7b + b2 + -96 + 7b + -1b2 Combine like terms: -19b + 7b = -12b -96 + -12b + 10b2 + -1b2 = 96 + -7b + b2 + -96 + 7b + -1b2 Combine like terms: 10b2 + -1b2 = 9b2 -96 + -12b + 9b2 = 96 + -7b + b2 + -96 + 7b + -1b2 Reorder the terms: -96 + -12b + 9b2 = 96 + -96 + -7b + 7b + b2 + -1b2 Combine like terms: 96 + -96 = 0 -96 + -12b + 9b2 = 0 + -7b + 7b + b2 + -1b2 -96 + -12b + 9b2 = -7b + 7b + b2 + -1b2 Combine like terms: -7b + 7b = 0 -96 + -12b + 9b2 = 0 + b2 + -1b2 -96 + -12b + 9b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 -96 + -12b + 9b2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-32 + -4b + 3b2) = 0 Factor a trinomial. 3((-8 + -3b)(4 + -1b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-8 + -3b)' equal to zero and attempt to solve: Simplifying -8 + -3b = 0 Solving -8 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3b = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3b = 0 + 8 -3b = 0 + 8 Combine like terms: 0 + 8 = 8 -3b = 8 Divide each side by '-3'. b = -2.666666667 Simplifying b = -2.666666667Subproblem 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 = {-2.666666667, 4}
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