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Simplifying 50 = b(b + -5) Reorder the terms: 50 = b(-5 + b) 50 = (-5 * b + b * b) 50 = (-5b + b2) Solving 50 = -5b + b2 Solving for variable 'b'. Reorder the terms: 50 + 5b + -1b2 = -5b + 5b + b2 + -1b2 Combine like terms: -5b + 5b = 0 50 + 5b + -1b2 = 0 + b2 + -1b2 50 + 5b + -1b2 = b2 + -1b2 Combine like terms: b2 + -1b2 = 0 50 + 5b + -1b2 = 0 Factor a trinomial. (10 + -1b)(5 + b) = 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 '(5 + b)' equal to zero and attempt to solve: Simplifying 5 + b = 0 Solving 5 + b = 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 + b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + b = 0 + -5 b = 0 + -5 Combine like terms: 0 + -5 = -5 b = -5 Simplifying b = -5Solution
b = {10, -5}
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