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Simplifying 4b2 = 10 + 18b Solving 4b2 = 10 + 18b Solving for variable 'b'. Reorder the terms: -10 + -18b + 4b2 = 10 + 18b + -10 + -18b Reorder the terms: -10 + -18b + 4b2 = 10 + -10 + 18b + -18b Combine like terms: 10 + -10 = 0 -10 + -18b + 4b2 = 0 + 18b + -18b -10 + -18b + 4b2 = 18b + -18b Combine like terms: 18b + -18b = 0 -10 + -18b + 4b2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -9b + 2b2) = 0 Factor a trinomial. 2((-1 + -2b)(5 + -1b)) = 0 Ignore the factor 2.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 + -1b)' equal to zero and attempt to solve: Simplifying 5 + -1b = 0 Solving 5 + -1b = 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 + -1b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1b = 0 + -5 -1b = 0 + -5 Combine like terms: 0 + -5 = -5 -1b = -5 Divide each side by '-1'. b = 5 Simplifying b = 5Solution
b = {-0.5, 5}
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