how do you solve a quadratic equation

Guest Mar 2, 2017

1+0 Answers


There are multiple ways to solve a quadratic equation. 3 common ways to solve a quadratic equation are by: factoring, completing the square, or using the quadratic formula. I highly recommond simply google searching how to solve a quadratic equation.


However here's an explaination on one of the methods:

Let's solve the quadratic equation using the factoring method: x2 + 2x + 1 = 0.

To factor, you simply try to find the multiples (the factors) of the c-value which is the coefficient of the number most commonly without an x and in this case the c-value is 1. So the factors of 1 are: 1 and 1. Now you do the same for the a-value which is the coefficient of the x2 value. In this case the a-value is also 1. The multiples of 1 are still: 1 and 1. Now you play around the with the factors (multiples) of the a and c value. What you want to do is that you want multiply one a-factor by one c-factor, then do the same for another a and c factor. Mess around with the multiplication until the sum of both products equals the b-value which in this case is 2 (the b-value is the coefficient next to the x). It helps to organize it like so:

1 x 1 = 1

1 x 1 = 1


On the left are the multiples of the a - value and on the right are the multiples of the c-value.

In this equation you don't have to mess around with it much because the sum of the factors already equals the b-value.

1 +1 = 2 (2 is our b-value).

So the factors of this equation are (x+1) (x+1). The solution is x =  -1; an easier way to explain this is to set both factors to zero then solve for x. (x+1 = 0).


Another example is: x2 +5x + 6.

Factors of the c-value: 1,2, 3, 6

Factors of the a-value: 1

Organize it:

1 1

1 2



Mess around with the multiplication and you'll get 2x1 = 2 and 3x1=3. Sum of both products is 3 + 2 = 5 (which is the b-value). Set both factors to zero: x +2 = 0. x+3 = 0. The solutions are: -3,-2. (or x = -2,-3)


Hope this helps!


Guest Mar 2, 2017

8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details