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Simplifying 4b2 + -16b = 84 Reorder the terms: -16b + 4b2 = 84 Solving -16b + 4b2 = 84 Solving for variable 'b'. Reorder the terms: -84 + -16b + 4b2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + -16b + 4b2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + -4b + b2) = 0 Factor a trinomial. 4((-3 + -1b)(7 + -1b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -1b)' equal to zero and attempt to solve: Simplifying -3 + -1b = 0 Solving -3 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1b = 0 + 3 -1b = 0 + 3 Combine like terms: 0 + 3 = 3 -1b = 3 Divide each side by '-1'. b = -3 Simplifying b = -3Subproblem 2
Set the factor '(7 + -1b)' equal to zero and attempt to solve: Simplifying 7 + -1b = 0 Solving 7 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1b = 0 + -7 -1b = 0 + -7 Combine like terms: 0 + -7 = -7 -1b = -7 Divide each side by '-1'. b = 7 Simplifying b = 7Solution
b = {-3, 7}
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