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Simplifying b2 + -2b = 40 + 4b Reorder the terms: -2b + b2 = 40 + 4b Solving -2b + b2 = 40 + 4b Solving for variable 'b'. Reorder the terms: -40 + -2b + -4b + b2 = 40 + 4b + -40 + -4b Combine like terms: -2b + -4b = -6b -40 + -6b + b2 = 40 + 4b + -40 + -4b Reorder the terms: -40 + -6b + b2 = 40 + -40 + 4b + -4b Combine like terms: 40 + -40 = 0 -40 + -6b + b2 = 0 + 4b + -4b -40 + -6b + b2 = 4b + -4b Combine like terms: 4b + -4b = 0 -40 + -6b + b2 = 0 Factor a trinomial. (-4 + -1b)(10 + -1b) = 0Subproblem 1
Set the factor '(-4 + -1b)' equal to zero and attempt to solve: Simplifying -4 + -1b = 0 Solving -4 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1b = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1b = 0 + 4 -1b = 0 + 4 Combine like terms: 0 + 4 = 4 -1b = 4 Divide each side by '-1'. b = -4 Simplifying b = -4Subproblem 2
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 = 10Solution
b = {-4, 10}
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