Final answer:
To solve the quadratic equation 2c² = 338, divide by 2 and then take the square root to find c = 13 or c = -13.
Step-by-step explanation:
To solve for c in the equation 2c² = 338, we first need to rewrite the equation in a standard quadratic form, which is ax² + bx + c = 0. For this equation, we need to divide through by 2 to isolate c², which gives us c² = 169. Taking the square root of both sides, we get two possible solutions for c since a squared number can have both a positive and a negative square root. The solutions are c = √169 and c = -√169, which simplifies to c = 13 or c = -13.