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

Question

asked Nov 11, 2021 232k views

1 Answer

Shava · Answer 1 · 2021-11-17T16:44:34+0000

Answer:

$x=-4\pm\sqrt5$

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 :)