Question

What is the intermediate step in the form (x + a)2 = b as a result of completing the

square for the following equation?
x^2-7x = -9x – 2

Answer 1

Step-by-step explanation

Since we have the expression:

(x + a)^2 = b

And the quadratic expression:

`x^2-7x\text{ = -9x - 2}`

Adding +2 to both sides:

`x^2-7x\text{ +2 = -9x}`

Adding +9x to both sides:

`x^2+2x+2=0`

Now, rewriting the expression:

`x^2+2x=-2`

Now, completing the square of:

`x^2+bx=c`

We need to add b^2/4 to both sides:

`(2^2)/(4)=(4)/(4)=1`

Now, we get:

`x^2+2x+1=-2+1`

and get:

`(x+1)^2=-1`

Therefore, we need to take square roots of the expression to get:

`√((x+1)^2)=√(-1)`
`x+1=i`

Isolating x:

`x=-1\pm i`

Therefore:

`x^2+2x+2=`
`=(-1+i)(-1-i)`