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Simplifying 1 = 4c2 + 7c + -14 Reorder the terms: 1 = -14 + 7c + 4c2 Solving 1 = -14 + 7c + 4c2 Solving for variable 'c'. Combine like terms: 1 + 14 = 15 15 + -7c + -4c2 = -14 + 7c + 4c2 + 14 + -7c + -4c2 Reorder the terms: 15 + -7c + -4c2 = -14 + 14 + 7c + -7c + 4c2 + -4c2 Combine like terms: -14 + 14 = 0 15 + -7c + -4c2 = 0 + 7c + -7c + 4c2 + -4c2 15 + -7c + -4c2 = 7c + -7c + 4c2 + -4c2 Combine like terms: 7c + -7c = 0 15 + -7c + -4c2 = 0 + 4c2 + -4c2 15 + -7c + -4c2 = 4c2 + -4c2 Combine like terms: 4c2 + -4c2 = 0 15 + -7c + -4c2 = 0 Factor a trinomial. (5 + -4c)(3 + c) = 0Subproblem 1
Set the factor '(5 + -4c)' equal to zero and attempt to solve: Simplifying 5 + -4c = 0 Solving 5 + -4c = 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 + -4c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4c = 0 + -5 -4c = 0 + -5 Combine like terms: 0 + -5 = -5 -4c = -5 Divide each side by '-4'. c = 1.25 Simplifying c = 1.25Subproblem 2
Set the factor '(3 + c)' equal to zero and attempt to solve: Simplifying 3 + c = 0 Solving 3 + c = 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 + c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + c = 0 + -3 c = 0 + -3 Combine like terms: 0 + -3 = -3 c = -3 Simplifying c = -3Solution
c = {1.25, -3}
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