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Simplifying 140 = 265b + -35b2 Solving 140 = 265b + -35b2 Solving for variable 'b'. Reorder the terms: 140 + -265b + 35b2 = 265b + -265b + -35b2 + 35b2 Combine like terms: 265b + -265b = 0 140 + -265b + 35b2 = 0 + -35b2 + 35b2 140 + -265b + 35b2 = -35b2 + 35b2 Combine like terms: -35b2 + 35b2 = 0 140 + -265b + 35b2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(28 + -53b + 7b2) = 0 Factor a trinomial. 5((4 + -7b)(7 + -1b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + -7b)' equal to zero and attempt to solve: Simplifying 4 + -7b = 0 Solving 4 + -7b = 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 + -7b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7b = 0 + -4 -7b = 0 + -4 Combine like terms: 0 + -4 = -4 -7b = -4 Divide each side by '-7'. b = 0.5714285714 Simplifying b = 0.5714285714Subproblem 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 = {0.5714285714, 7}
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