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Simplifying 4b2 + -12b + 9 = 169 Reorder the terms: 9 + -12b + 4b2 = 169 Solving 9 + -12b + 4b2 = 169 Solving for variable 'b'. Reorder the terms: 9 + -169 + -12b + 4b2 = 169 + -169 Combine like terms: 9 + -169 = -160 -160 + -12b + 4b2 = 169 + -169 Combine like terms: 169 + -169 = 0 -160 + -12b + 4b2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-40 + -3b + b2) = 0 Factor a trinomial. 4((-5 + -1b)(8 + -1b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -1b)' equal to zero and attempt to solve: Simplifying -5 + -1b = 0 Solving -5 + -1b = 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 + -1b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1b = 0 + 5 -1b = 0 + 5 Combine like terms: 0 + 5 = 5 -1b = 5 Divide each side by '-1'. b = -5 Simplifying b = -5Subproblem 2
Set the factor '(8 + -1b)' equal to zero and attempt to solve: Simplifying 8 + -1b = 0 Solving 8 + -1b = 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 + -1b = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1b = 0 + -8 -1b = 0 + -8 Combine like terms: 0 + -8 = -8 -1b = -8 Divide each side by '-1'. b = 8 Simplifying b = 8Solution
b = {-5, 8}
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