Since the coefficient of the variable x is positive (+2), we will use the form:
[tex](x+a)^2=b_{}[/tex]
(That is, first option/form)
Then, to solve the equation by completing the square, since the coefficient of the variable x is 2, we need the number (2/2)^2 to show up, that is, number 1:
[tex]\begin{gathered} x^2+2x-5=0 \\ x^2+2x+1-1-5=0 \\ (x+1)^2-1-5=0 \\ (x+1)^2-6=0^{} \\ (x+1)^2=6 \end{gathered}[/tex]
So the missing numbers in the first option are 1 and 6. Then, solving the equation, we have:
[tex]\begin{gathered} (x+1)^2=6 \\ x+1=\pm\sqrt[]{6} \\ \begin{cases}x+1=\sqrt[]{6}\to x=\sqrt[]{6}-1 \\ x+1=-\sqrt[]{6}\to x=-\sqrt[]{6}-1\end{cases} \end{gathered}[/tex]
So the solutions are x = √6 - 1 , -√6 - 1
