Question

Solve for x using the Quadratic Formula: x2 + 2x + 1 = 0 x equals negative b plus or minus the square root of b squared minus 4 times a times c, all over 2 times a

x = 2
x = 1
x = 0
x = −1

Answer 1

X=-1

You can factor this because it is already a perfect square. you can check this by seeing if half of b squared is equal to c.

In this problem
a=1
b=2
c=1
Half of b is 1
1 squared is 1

After that you just break it down

There’s 2 x so,

(x+_)(x+_)
The blank is just half of b which we already found to be 1

So,
(x+1)(x+1)

Also can be written as (x+1)^2

Set both parenthesis equal to 0
(In this case you only have to do it once since it’s the same value)

x+1=0
x=-1

Another way to factor is to see if there are two numbers that result in c when multiplied and result in b when added.
In this case it’s 1 and 1
So you just factor out the x and the ones

(x+1)(x+1)
Which will give you the same answer.

(If you get used to factoring, it’s quicker to use)

X=-1

Answer 2

x = - 1

Explanation:

x² + 2x + 1 = 0

Using the quadratic formula

`x = \frac{ - b± \sqrt{ {b}^(2) - 4ac } }{2a}`

a = 1 , b = 2 , c = 1

We have

`x = \frac{ - 2± \sqrt{ {2}^(2) - 4(1)(1)} }{2(1)} \\ \\ x = ( - 2 ± √(4 - 4) )/(2) \\ \\ x = ( - 2 ± √(0) )/(2) \\ \\ x = - (2)/(2) \\ \\ x = - 1`

Hope this helps you