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Simplifying 0 = 9b2 + -48b + 64 Reorder the terms: 0 = 64 + -48b + 9b2 Solving 0 = 64 + -48b + 9b2 Solving for variable 'b'. Combine like terms: 0 + -64 = -64 -64 + 48b + -9b2 = 64 + -48b + 9b2 + -64 + 48b + -9b2 Reorder the terms: -64 + 48b + -9b2 = 64 + -64 + -48b + 48b + 9b2 + -9b2 Combine like terms: 64 + -64 = 0 -64 + 48b + -9b2 = 0 + -48b + 48b + 9b2 + -9b2 -64 + 48b + -9b2 = -48b + 48b + 9b2 + -9b2 Combine like terms: -48b + 48b = 0 -64 + 48b + -9b2 = 0 + 9b2 + -9b2 -64 + 48b + -9b2 = 9b2 + -9b2 Combine like terms: 9b2 + -9b2 = 0 -64 + 48b + -9b2 = 0 Factor a trinomial. (-8 + 3b)(8 + -3b) = 0Subproblem 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 '(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 = 2.666666667Solution
b = {2.666666667, 2.666666667}
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