Sometimes, you might run into quadratics that you can't quite factor. There is also completing the square, but that can take a long time. The quadratic formula is a simple and easy formula that you can plug values into to get an output
ISAIAH LOPEZ
As you probably already know, the standard form of a quadratic equation is ax² + bx + c = 0. The quadratic formula uses these letters, so make sure you know the standard form of a quadratic equation first. The quadratic formula is somewhat complicated, but it gets easier over time once you've memorized it. The quadratic formula is shown below.
Now that you know the formula, let's do an example. Let's use the equation 6x² + 19x - 7 = 0. In this equation, a = 6, b = 19, and c = -7. (Make sure not to forget that c is -7 and not 7 because of the minus sign.) We can now plug in our values and solve the equation.
We could then simplify this expression for x to equal the expression below.
Now that we have this general form, we can simplify even farther to get that x = 1/3 or -7/2. You won't always be able to simplify, however, so it's okay to leave it like this for those problems.
It is actually possible to factor every quadratic equation. This would be very long-winded, however, and would take a lot more time than using the quadratic formula. Another thing to note is that some more complex equations have big numbers, fractional values, or even irrational numbers. These are almost impossible to factor without using the quadratic formula, so hopefully you understood this lesson.