Here I'm going to show you how to solve basic quadratic equations. Here's our question:
Solve x2 + 5x + 4 = 0.
An important point here is that quadratic equations must equal 0. If they don't, you'll have to rearrange them so they do. Now we're going to factorise the equation. If you don't know how to do this, see my post on that.
(x + 4)(x + 1) = 0
Now, we use simple common sense. One bracket times the other bracket is 0. The only way that can happen is if one of them is 0. So either x + 4 or x + 1 is 0. If x + 4 = 0:
x + 4 = 0
x = 0 - 4
x = -4
If x + 1 = 0:
x + 1 = 0
x = 0 - 1
x = -1
So x is either -4 or -1. We can't actually find which of these it is, but that doesn't matter. If you prefer the simpler method, you can simply take the numbers added to the x (4 and 1) and reverse their signs to get -4 and -1.
We will do more complex quadratics soon. In the meantime, you can test yourself on these:
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