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Simplifying (b + 2 + b)(10b + 20 + b) = 1204 Reorder the terms: (2 + b + b)(10b + 20 + b) = 1204 Combine like terms: b + b = 2b (2 + 2b)(10b + 20 + b) = 1204 Reorder the terms: (2 + 2b)(20 + 10b + b) = 1204 Combine like terms: 10b + b = 11b (2 + 2b)(20 + 11b) = 1204 Multiply (2 + 2b) * (20 + 11b) (2(20 + 11b) + 2b * (20 + 11b)) = 1204 ((20 * 2 + 11b * 2) + 2b * (20 + 11b)) = 1204 ((40 + 22b) + 2b * (20 + 11b)) = 1204 (40 + 22b + (20 * 2b + 11b * 2b)) = 1204 (40 + 22b + (40b + 22b2)) = 1204 Combine like terms: 22b + 40b = 62b (40 + 62b + 22b2) = 1204 Solving 40 + 62b + 22b2 = 1204 Solving for variable 'b'. Reorder the terms: 40 + -1204 + 62b + 22b2 = 1204 + -1204 Combine like terms: 40 + -1204 = -1164 -1164 + 62b + 22b2 = 1204 + -1204 Combine like terms: 1204 + -1204 = 0 -1164 + 62b + 22b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-582 + 31b + 11b2) = 0 Factor a trinomial. 2((-97 + -11b)(6 + -1b)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-97 + -11b)' equal to zero and attempt to solve: Simplifying -97 + -11b = 0 Solving -97 + -11b = 0 Move all terms containing b to the left, all other terms to the right. Add '97' to each side of the equation. -97 + 97 + -11b = 0 + 97 Combine like terms: -97 + 97 = 0 0 + -11b = 0 + 97 -11b = 0 + 97 Combine like terms: 0 + 97 = 97 -11b = 97 Divide each side by '-11'. b = -8.818181818 Simplifying b = -8.818181818Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve: Simplifying 6 + -1b = 0 Solving 6 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1b = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1b = 0 + -6 -1b = 0 + -6 Combine like terms: 0 + -6 = -6 -1b = -6 Divide each side by '-1'. b = 6 Simplifying b = 6Solution
b = {-8.818181818, 6}
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