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Simplifying 7c2 + -14c + 8 = 64 Reorder the terms: 8 + -14c + 7c2 = 64 Solving 8 + -14c + 7c2 = 64 Solving for variable 'c'. Reorder the terms: 8 + -64 + -14c + 7c2 = 64 + -64 Combine like terms: 8 + -64 = -56 -56 + -14c + 7c2 = 64 + -64 Combine like terms: 64 + -64 = 0 -56 + -14c + 7c2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-8 + -2c + c2) = 0 Factor a trinomial. 7((-2 + -1c)(4 + -1c)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-2 + -1c)' equal to zero and attempt to solve: Simplifying -2 + -1c = 0 Solving -2 + -1c = 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 + -1c = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1c = 0 + 2 -1c = 0 + 2 Combine like terms: 0 + 2 = 2 -1c = 2 Divide each side by '-1'. c = -2 Simplifying c = -2Subproblem 2
Set the factor '(4 + -1c)' equal to zero and attempt to solve: Simplifying 4 + -1c = 0 Solving 4 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1c = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1c = 0 + -4 -1c = 0 + -4 Combine like terms: 0 + -4 = -4 -1c = -4 Divide each side by '-1'. c = 4 Simplifying c = 4Solution
c = {-2, 4}
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