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Simplifying 0 = 27b + -5b2 + -10 Reorder the terms: 0 = -10 + 27b + -5b2 Solving 0 = -10 + 27b + -5b2 Solving for variable 'b'. Combine like terms: 0 + 10 = 10 10 + -27b + 5b2 = -10 + 27b + -5b2 + 10 + -27b + 5b2 Reorder the terms: 10 + -27b + 5b2 = -10 + 10 + 27b + -27b + -5b2 + 5b2 Combine like terms: -10 + 10 = 0 10 + -27b + 5b2 = 0 + 27b + -27b + -5b2 + 5b2 10 + -27b + 5b2 = 27b + -27b + -5b2 + 5b2 Combine like terms: 27b + -27b = 0 10 + -27b + 5b2 = 0 + -5b2 + 5b2 10 + -27b + 5b2 = -5b2 + 5b2 Combine like terms: -5b2 + 5b2 = 0 10 + -27b + 5b2 = 0 Factor a trinomial. (2 + -5b)(5 + -1b) = 0Subproblem 1
Set the factor '(2 + -5b)' equal to zero and attempt to solve: Simplifying 2 + -5b = 0 Solving 2 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5b = 0 + -2 -5b = 0 + -2 Combine like terms: 0 + -2 = -2 -5b = -2 Divide each side by '-5'. b = 0.4 Simplifying b = 0.4Subproblem 2
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 = 5Solution
b = {0.4, 5}
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