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Simplifying 2(4c2 + 9 + 12c) = c2 + 15c + 64 Reorder the terms: 2(9 + 12c + 4c2) = c2 + 15c + 64 (9 * 2 + 12c * 2 + 4c2 * 2) = c2 + 15c + 64 (18 + 24c + 8c2) = c2 + 15c + 64 Reorder the terms: 18 + 24c + 8c2 = 64 + 15c + c2 Solving 18 + 24c + 8c2 = 64 + 15c + c2 Solving for variable 'c'. Reorder the terms: 18 + -64 + 24c + -15c + 8c2 + -1c2 = 64 + 15c + c2 + -64 + -15c + -1c2 Combine like terms: 18 + -64 = -46 -46 + 24c + -15c + 8c2 + -1c2 = 64 + 15c + c2 + -64 + -15c + -1c2 Combine like terms: 24c + -15c = 9c -46 + 9c + 8c2 + -1c2 = 64 + 15c + c2 + -64 + -15c + -1c2 Combine like terms: 8c2 + -1c2 = 7c2 -46 + 9c + 7c2 = 64 + 15c + c2 + -64 + -15c + -1c2 Reorder the terms: -46 + 9c + 7c2 = 64 + -64 + 15c + -15c + c2 + -1c2 Combine like terms: 64 + -64 = 0 -46 + 9c + 7c2 = 0 + 15c + -15c + c2 + -1c2 -46 + 9c + 7c2 = 15c + -15c + c2 + -1c2 Combine like terms: 15c + -15c = 0 -46 + 9c + 7c2 = 0 + c2 + -1c2 -46 + 9c + 7c2 = c2 + -1c2 Combine like terms: c2 + -1c2 = 0 -46 + 9c + 7c2 = 0 Factor a trinomial. (-23 + -7c)(2 + -1c) = 0Subproblem 1
Set the factor '(-23 + -7c)' equal to zero and attempt to solve: Simplifying -23 + -7c = 0 Solving -23 + -7c = 0 Move all terms containing c to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + -7c = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -7c = 0 + 23 -7c = 0 + 23 Combine like terms: 0 + 23 = 23 -7c = 23 Divide each side by '-7'. c = -3.285714286 Simplifying c = -3.285714286Subproblem 2
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 = 2Solution
c = {-3.285714286, 2}
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