Given:
[tex]x^2+10x+27=0[/tex]Required:
To complete the square that leads to the equivalent equation (x +__ )^2 = __.
Explanation:
Consider
[tex]\begin{gathered} x^2+10x+27=0 \\ \\ x^2+10x+25+2=0 \\ \\ x^2+10x+25=-2 \\ \\ x^2+5x+5x+25=-2 \\ \\ x(x+5)+5(x+5)=-2 \\ \\ (x+5)(x+5)=-2 \\ \\ (x+5)^2=-2 \end{gathered}[/tex]Final Answer:
[tex](x+5)^{2}=-2[/tex]