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Simplifying 14b4 + -23b3 + 8b2 = 0 Reorder the terms: 8b2 + -23b3 + 14b4 = 0 Solving 8b2 + -23b3 + 14b4 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), 'b2'. b2(8 + -23b + 14b2) = 0 Factor a trinomial. b2((1 + -2b)(8 + -7b)) = 0Subproblem 1
Set the factor 'b2' equal to zero and attempt to solve: Simplifying b2 = 0 Solving b2 = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b2 = 0 Take the square root of each side: b = {0}Subproblem 2
Set the factor '(1 + -2b)' equal to zero and attempt to solve: Simplifying 1 + -2b = 0 Solving 1 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2b = 0 + -1 -2b = 0 + -1 Combine like terms: 0 + -1 = -1 -2b = -1 Divide each side by '-2'. b = 0.5 Simplifying b = 0.5Subproblem 3
Set the factor '(8 + -7b)' equal to zero and attempt to solve: Simplifying 8 + -7b = 0 Solving 8 + -7b = 0 Move all terms containing b to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7b = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7b = 0 + -8 -7b = 0 + -8 Combine like terms: 0 + -8 = -8 -7b = -8 Divide each side by '-7'. b = 1.142857143 Simplifying b = 1.142857143Solution
b = {0, 0.5, 1.142857143}
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