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Simplifying 12c2 = 45 + 51c Solving 12c2 = 45 + 51c Solving for variable 'c'. Reorder the terms: -45 + -51c + 12c2 = 45 + 51c + -45 + -51c Reorder the terms: -45 + -51c + 12c2 = 45 + -45 + 51c + -51c Combine like terms: 45 + -45 = 0 -45 + -51c + 12c2 = 0 + 51c + -51c -45 + -51c + 12c2 = 51c + -51c Combine like terms: 51c + -51c = 0 -45 + -51c + 12c2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + -17c + 4c2) = 0 Factor a trinomial. 3((-3 + -4c)(5 + -1c)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -4c)' equal to zero and attempt to solve: Simplifying -3 + -4c = 0 Solving -3 + -4c = 0 Move all terms containing c to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4c = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4c = 0 + 3 -4c = 0 + 3 Combine like terms: 0 + 3 = 3 -4c = 3 Divide each side by '-4'. c = -0.75 Simplifying c = -0.75Subproblem 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 = {-0.75, 5}
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