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Simplifying 243 = (4b + -9) * b Reorder the terms: 243 = (-9 + 4b) * b Reorder the terms for easier multiplication: 243 = b(-9 + 4b) 243 = (-9 * b + 4b * b) 243 = (-9b + 4b2) Solving 243 = -9b + 4b2 Solving for variable 'b'. Reorder the terms: 243 + 9b + -4b2 = -9b + 9b + 4b2 + -4b2 Combine like terms: -9b + 9b = 0 243 + 9b + -4b2 = 0 + 4b2 + -4b2 243 + 9b + -4b2 = 4b2 + -4b2 Combine like terms: 4b2 + -4b2 = 0 243 + 9b + -4b2 = 0 Factor a trinomial. (9 + -1b)(27 + 4b) = 0Subproblem 1
Set the factor '(9 + -1b)' equal to zero and attempt to solve: Simplifying 9 + -1b = 0 Solving 9 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1b = 0 + -9 -1b = 0 + -9 Combine like terms: 0 + -9 = -9 -1b = -9 Divide each side by '-1'. b = 9 Simplifying b = 9Subproblem 2
Set the factor '(27 + 4b)' equal to zero and attempt to solve: Simplifying 27 + 4b = 0 Solving 27 + 4b = 0 Move all terms containing b to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + 4b = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 4b = 0 + -27 4b = 0 + -27 Combine like terms: 0 + -27 = -27 4b = -27 Divide each side by '4'. b = -6.75 Simplifying b = -6.75Solution
b = {9, -6.75}
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