Question

Solve the quadratic equation by completing the square x^2+8x+11=0

Answer 1

`x=-4\pm\sqrt5`

Explanation:

So we have the equation:

`x^2+8x+11=0`

First, subtract 11 from both sides:

`x^2+8x=-11`

Now, add the c term. Divide 8 by 2 and then square it:

`(x^2+8x+16)=-11`

What we do to one side we must also do to the other. Thus:

`(x^2+8x+16)=-11+16`

Simplify:

`(x^2+8x+16)=5`

Perfect Square Trinomial:

`(x+4)^2=5`

Take the square root:

`x+4=\pm\sqrt5`

Subtract 4:

`x=-4\pm\sqrt5`

And that's our answer :)