The quadratic equation 2x^2-3=125 is being solved without quadratic formula, by completing the square.

Once we get:

x^2 = 2^6

we take the square root on both sides of the equation and get the solutions:

x1 = 2^(6/2)

x2 = - 2^(6/2)

That is 

x1 = 2^3

x1 = 8

x2 = -2^3

x2 = -8

You can obtain an explanation for any step by clicking on it. Please note that you cannot click on the very first expression, which is the original problem. Quite often, several transformations will be performed within the same step. Use the explanation navigation buttons to step through all of them:

If you are not satisfied with the number of solution steps displayed (either too many steps or too few), click on the Options button to adjust the number of steps to be shown. On the same screen, you can select integer or real arithmetics to be used during the solution process (e.g., x=1/2 vs. x=0.5). It is important to understand that if integer arithmetics is chosen, then all decimal numbers will be converted to integer fractions as part of the solution process. This may produce a solution that is long and somewhat confusing.