# How do I use the quadratic formula to solve x^2 + 7x = 3?

Sep 13, 2014

To do quadratic formula, you just need to know what to plug where.

However, before we get to the quadratic formula, we need to know the parts of our equation itself. You will see why this is important in a moment. So here's the standardised equation for a quadratic that you can solve with the quadratic formula:

$a {x}^{2} + b x + c = 0$

Now as you notice, we have the equation ${x}^{2} + 7 x = 3$, with the 3 on the other side of the equation. So to put it into standard form, we shall subtract 3 from both sides to get:

${x}^{2} + 7 x - 3 = 0$

So now that that's done, let's look at the quadratic formula itself:

$\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Now you understand why we needed to see the standardised form of the equation. Without that, we wouldn't know what they meant by a, b or c! So we now understand that they are simply our coefficients and constant. Hence in our case:

$a = 1$
$b = 7$
$c = - 3$

From here onwards it's not too bad. All we need to do is plug in the values:

$\frac{- 7 \pm \sqrt{{\left(7\right)}^{2} - 4 \left(1\right) \left(- 3\right)}}{2 \left(1\right)}$

Make sure you solve for both the plus and the minus. Our answers are: -7.4 and 0.4.

In the end, always plug your answers back into your original equation to see if they work. This not only helps you check if you did the problem right, but it also helps you weed out any extraneous solutions you may get.

In this case, only the 2nd answer (0.4) works.

Here is a video that explains this as well.

Hope that helps :)