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Simplifying 7b2 + -21b = 196 Reorder the terms: -21b + 7b2 = 196 Solving -21b + 7b2 = 196 Solving for variable 'b'. Reorder the terms: -196 + -21b + 7b2 = 196 + -196 Combine like terms: 196 + -196 = 0 -196 + -21b + 7b2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-28 + -3b + b2) = 0 Factor a trinomial. 7((-4 + -1b)(7 + -1b)) = 0 Ignore the factor 7.Subproblem 1
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 = -4Subproblem 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 = {-4, 7}
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