Final answer:
To find the GCF of the quadratic equation 6x^2 - 6 = 0, factor out the GCF, and find the solutions, we first identify the GCF. Then, we factor out the GCF from the equation and set each factor equal to zero. Finally, we solve for x to find the solutions.
Step-by-step explanation:
To find the GCF (Greatest Common Factor) of the quadratic equation 6x^2 - 6 = 0, we need to factor out the common factor from the terms. In this case, the GCF is 6 because it is the highest number that divides both 6x^2 and 6 evenly.
Factoring out the GCF, we have:
6(x^2 - 1) = 0
To find the solutions, we set each factor equal to zero:
x^2 - 1 = 0
x^2 = 1
Taking the square root of both sides gives us:
x = 1 or x = -1
Therefore, the solutions to the quadratic equation 6x^2 - 6 = 0 are x = 1 and x = -1.