Question

4^k=x^2+8x
please help solve in terms of x please.

Answer 1

Okay so, its a quadratic equation because the highest power of x is 2. So lets 'complete the square'.
\[x^2+8x=4^k\]
So add half the coefficient of x to both side, so the equation is still equal.
\[(x^2+8x+4^2)=4^k+4^2\]
Now its a perfect square. So therefore:
\[(x+4)^2=4^k+16\]
Now we just simplify.
\[x+4=\pm\sqrt(4k+16)\]
And again.
\[x=-4\pm4\sqrt(4^k)\]

Answer 2

thank youuuu!

Answer 3

oh right i meant "add the square of half the coefficient of x". :-)