Let's solve the equation step by step. First, square the expression on the right side of the equation: (4c-5+1)^2 = 16c^2 - 40c + 26c - 25 + 10 - 1 = 16c^2 - 14c - 16 Now, we can rewrite the equation: 4c - 5 + 1 = 16c^2 - 14c - 16 Combine like terms: 4c - 4 = 16c^2 - 14c - 16 Move all terms to one side of the equation: 16c^2 - 18c - 12 = 0 Divide the equation by the common factor of 2: 8c^2 - 9c - 6 = 0 Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. However, this equation does not factor easily, so we will use the quadratic formula: c = (-b ± √(b^2 - 4ac)) / 2a For this equation, a = 8, b = -9, and c = -6. Plugging in these values, we have: c = (-(-9) ± √((-9)^2 - 4(8)(-6))) / (2(8)) c = (9 ± √(81 + 192)) / 16 c = (9 ± √273) / 16 Therefore, c is equal to either (9 + √273) / 16 or (9 - √273) / 16.

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