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Simplifying 14c4 + -23c3 + 8c2 = 0 Reorder the terms: 8c2 + -23c3 + 14c4 = 0 Solving 8c2 + -23c3 + 14c4 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), 'c2'. c2(8 + -23c + 14c2) = 0 Factor a trinomial. c2((1 + -2c)(8 + -7c)) = 0Subproblem 1
Set the factor 'c2' equal to zero and attempt to solve: Simplifying c2 = 0 Solving c2 = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c2 = 0 Take the square root of each side: c = {0}Subproblem 2
Set the factor '(1 + -2c)' equal to zero and attempt to solve: Simplifying 1 + -2c = 0 Solving 1 + -2c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2c = 0 + -1 -2c = 0 + -1 Combine like terms: 0 + -1 = -1 -2c = -1 Divide each side by '-2'. c = 0.5 Simplifying c = 0.5Subproblem 3
Set the factor '(8 + -7c)' equal to zero and attempt to solve: Simplifying 8 + -7c = 0 Solving 8 + -7c = 0 Move all terms containing c to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -7c = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7c = 0 + -8 -7c = 0 + -8 Combine like terms: 0 + -8 = -8 -7c = -8 Divide each side by '-7'. c = 1.142857143 Simplifying c = 1.142857143Solution
c = {0, 0.5, 1.142857143}
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