Question

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

Answer 1

Answer:

$x=-4\pm\sqrt5$

Step-by-step 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 :)