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Simplifying 25b2 + -90b + 81 = 441 Reorder the terms: 81 + -90b + 25b2 = 441 Solving 81 + -90b + 25b2 = 441 Solving for variable 'b'. Reorder the terms: 81 + -441 + -90b + 25b2 = 441 + -441 Combine like terms: 81 + -441 = -360 -360 + -90b + 25b2 = 441 + -441 Combine like terms: 441 + -441 = 0 -360 + -90b + 25b2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-72 + -18b + 5b2) = 0 Factor a trinomial. 5((-12 + -5b)(6 + -1b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-12 + -5b)' equal to zero and attempt to solve: Simplifying -12 + -5b = 0 Solving -12 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -5b = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -5b = 0 + 12 -5b = 0 + 12 Combine like terms: 0 + 12 = 12 -5b = 12 Divide each side by '-5'. b = -2.4 Simplifying b = -2.4Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve: Simplifying 6 + -1b = 0 Solving 6 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1b = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1b = 0 + -6 -1b = 0 + -6 Combine like terms: 0 + -6 = -6 -1b = -6 Divide each side by '-1'. b = 6 Simplifying b = 6Solution
b = {-2.4, 6}
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