Question

Solve the quadratic equation by completing the square.

Answer 1

If we add 15 to both sides, we get

$x^2+8x+16=15$

We can read the left hand side as

$x^2 + 2\cdot 4\cdot x+4^2 = (x+4)^2$

So, the equation becomes

$(x+4)^2=15$

Take the square root of both sides:

$x+4 = \pm\sqrt{15}$

Subtract 4 from both sides:

$x=\pm\sqrt{15}-4$