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Simplifying 20b2 + -40b = 25 Reorder the terms: -40b + 20b2 = 25 Solving -40b + 20b2 = 25 Solving for variable 'b'. Reorder the terms: -25 + -40b + 20b2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -40b + 20b2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + -8b + 4b2) = 0 Factor a trinomial. 5((-1 + -2b)(5 + -2b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + -2b)' equal to zero and attempt to solve: Simplifying -1 + -2b = 0 Solving -1 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2b = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2b = 0 + 1 -2b = 0 + 1 Combine like terms: 0 + 1 = 1 -2b = 1 Divide each side by '-2'. b = -0.5 Simplifying b = -0.5Subproblem 2
Set the factor '(5 + -2b)' equal to zero and attempt to solve: Simplifying 5 + -2b = 0 Solving 5 + -2b = 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 + -2b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2b = 0 + -5 -2b = 0 + -5 Combine like terms: 0 + -5 = -5 -2b = -5 Divide each side by '-2'. b = 2.5 Simplifying b = 2.5Solution
b = {-0.5, 2.5}
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