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Simplifying 25b + 9b(4 + b) = 290 25b + (4 * 9b + b * 9b) = 290 25b + (36b + 9b2) = 290 Combine like terms: 25b + 36b = 61b 61b + 9b2 = 290 Solving 61b + 9b2 = 290 Solving for variable 'b'. Reorder the terms: -290 + 61b + 9b2 = 290 + -290 Combine like terms: 290 + -290 = 0 -290 + 61b + 9b2 = 0 Factor a trinomial. (-10 + -1b)(29 + -9b) = 0Subproblem 1
Set the factor '(-10 + -1b)' equal to zero and attempt to solve: Simplifying -10 + -1b = 0 Solving -10 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1b = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1b = 0 + 10 -1b = 0 + 10 Combine like terms: 0 + 10 = 10 -1b = 10 Divide each side by '-1'. b = -10 Simplifying b = -10Subproblem 2
Set the factor '(29 + -9b)' equal to zero and attempt to solve: Simplifying 29 + -9b = 0 Solving 29 + -9b = 0 Move all terms containing b to the left, all other terms to the right. Add '-29' to each side of the equation. 29 + -29 + -9b = 0 + -29 Combine like terms: 29 + -29 = 0 0 + -9b = 0 + -29 -9b = 0 + -29 Combine like terms: 0 + -29 = -29 -9b = -29 Divide each side by '-9'. b = 3.222222222 Simplifying b = 3.222222222Solution
b = {-10, 3.222222222}
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