[Math] by completing the square find in terms of k the roots of the equation $x^2 + 2kx-7=0$

Question

By completing the square find in terms of $k$ the roots of the equation $$x^2 + 2kx-7=0$$
prove for all real values of $k$, the roots are real

Answer 1

$$x^2+2kx-7=x^2+2\cdot x\cdot k+k^2-k^2-7=0$$ $$(x+k)^2=k^2+7$$ $$x+k=\pm\sqrt{k^2+7}$$ $$x=-k\pm\sqrt{k^2+7}$$ because $k^2+7\geq 0$ for all real $k$ all roots are real.