Question

Completing the square process, I don't quite understand it yet, can someone explain step by step? X^2+10x+16=0

Answer 1

`color(blue)(x=-8 " and " x=-2)`

Explanation:

`x^2+10x+16=0`

Step 1.

Divide right through by the coefficient of `x^2` if this is not 1.

We have a coefficient of 1, so we don't need to do this.

Step 2.

Move the constant to the `RHS`

`x^2+10x=-16`

Step 3.

Add to both sides the square of half the coefficient of `x`.

In this example this is `(5)^2` do not expand this, i.e. don't add it as 25.

`x^2+10x+(5)^2=-16+(5)^2`

Step 4.

Form a binomial on the `LHS`

Take away the `10x` to get:

`x^2+(5)^2`

Then we have:

`(x+5)^2`

And all together:

`(x+5)^2=-16+(5)^2`

Step 5.

Simplify `RHS`

`(x+5)^2=-16+25`

`(x+5)^2=9`

Step 6.

Take the square root of both sides:

`sqrt((x+5)^2)=sqrt(9)`

`x+5=+-3`

i.e.

`x+5=+3`

`x+5=-3`

Step 7.

Subtract five from both sides:

`x=-3-5=-8`

`x=3-5=-2`

So the solutions are:

`x=-8 and x=-2`