x^2 + 6x + 4 = 0
1) x^2 + 6x + ____ = - 4 All we did was move 4 to the other side. Then left a little empty space.
2) Using the formula (b/2)^2 in this formula please simplify the inside first then square it.
3) We need to find what b is. Well a b and c are just coefficients attached next to the variables. So in our case, a is next to x^2 which is 1, b is next to 6x which is just 6, etc.
4) Let's apply the formula from step 2. We have:
(b/2)^2 = (6/2)^2 = (3)^2 = 3 x 3 = 9 Now 9 is our new "c" we will add 9 to the "empty space" and with the other side to balance out the equation. It will look something like this.
5) x^2 + 6x + 9 = - 4 + 9
x^2 + 6x + 9 = 5
Now let's use the regular factoring method to solve this quadratic equation.
6) What two numbers when multiplied give you 9 but when you add them give you 6?
Well let's see: 1 x 9 = 9 , 1 + 9 = 10. This does not work because when you add the factors they don't give you 6.
Let's try out another pair: 3 x 3 = 9 and 3 + 3 = 6. This works!!! Yayayayay! lol!
We will use this now!
7) Our factors are: (x+3) (x+3) = 5
We can simplify this and write: (x+3)^2 = 5
Now let's solve for x.
8) To get rid of the "square" we have to take the square root on both sides. We get:
((x+3)^2)^(1/2) = (5)^(1/2) ...... I'm just writing the square root as an exponent. You can also use a square root symbol. Whichever works for you :)
9) We get: (x+3)^(2/2) = (5)^(1/2) or sqt of (5)
(x+3) = (5)^(1/2) or sqt of (5)
subtract 3 on both sides to leave x by itself.
x = - 3 + - (5)^(1/2) or sqt of (5)
this is + or -
The reason why we put + or - is because when solving for x, the square root almost always gives us + or - .
Anyways, your answer is: x = - 3 - (5)^(1/2) or sqt of (5) and - 3 + (5)^(1/2) or sqt of (5)
I hope this helps! Reach out for a extra help :)
