Solve Quadratics on the ASVAB AFQT Using the Quadratic Formula

By Rod Powers

Quadratic equations on the ASVAB AFQT can often be solved with the square-root method (when they’re simple) or the factoring method (as long as a = 1 in the form, ax2 + bx + c = 0).

But what if they’re more complicated? And what if you try to use the factoring method, but you find that a doesn’t equal 1, or that you can’t easily find two numbers that multiply to c and add up to b?

In these cases, you can rely on the quadratic formula to solve any quadratic equation. So why not just use the quadratic formula and forget about the square-root and factoring methods? Because the quadratic formula is kind of complex:


The quadratic formula uses the a, b, and c from ax2 + bx + c = 0, just like the factoring method.

Armed with this knowledge, you can apply your skills to a complex quadratic equation:

Solve: 2x2 – 4x – 3 = 0

In this equation, a = 2, b = –4, and c = –3. Plug the known values into the quadratic formula and simplify: