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Simplifying 4b2 = -3b + 76 Reorder the terms: 4b2 = 76 + -3b Solving 4b2 = 76 + -3b Solving for variable 'b'. Reorder the terms: -76 + 3b + 4b2 = 76 + -3b + -76 + 3b Reorder the terms: -76 + 3b + 4b2 = 76 + -76 + -3b + 3b Combine like terms: 76 + -76 = 0 -76 + 3b + 4b2 = 0 + -3b + 3b -76 + 3b + 4b2 = -3b + 3b Combine like terms: -3b + 3b = 0 -76 + 3b + 4b2 = 0 Factor a trinomial. (-19 + -4b)(4 + -1b) = 0Subproblem 1
Set the factor '(-19 + -4b)' equal to zero and attempt to solve: Simplifying -19 + -4b = 0 Solving -19 + -4b = 0 Move all terms containing b to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -4b = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -4b = 0 + 19 -4b = 0 + 19 Combine like terms: 0 + 19 = 19 -4b = 19 Divide each side by '-4'. b = -4.75 Simplifying b = -4.75Subproblem 2
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 = 4Solution
b = {-4.75, 4}
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