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Simplifying 12c2 = 40 + 52c Solving 12c2 = 40 + 52c Solving for variable 'c'. Reorder the terms: -40 + -52c + 12c2 = 40 + 52c + -40 + -52c Reorder the terms: -40 + -52c + 12c2 = 40 + -40 + 52c + -52c Combine like terms: 40 + -40 = 0 -40 + -52c + 12c2 = 0 + 52c + -52c -40 + -52c + 12c2 = 52c + -52c Combine like terms: 52c + -52c = 0 -40 + -52c + 12c2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + -13c + 3c2) = 0 Factor a trinomial. 4((-2 + -3c)(5 + -1c)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -3c)' equal to zero and attempt to solve: Simplifying -2 + -3c = 0 Solving -2 + -3c = 0 Move all terms containing c to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -3c = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3c = 0 + 2 -3c = 0 + 2 Combine like terms: 0 + 2 = 2 -3c = 2 Divide each side by '-3'. c = -0.6666666667 Simplifying c = -0.6666666667Subproblem 2
Set the factor '(5 + -1c)' equal to zero and attempt to solve: Simplifying 5 + -1c = 0 Solving 5 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1c = 0 + -5 -1c = 0 + -5 Combine like terms: 0 + -5 = -5 -1c = -5 Divide each side by '-1'. c = 5 Simplifying c = 5Solution
c = {-0.6666666667, 5}
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