[tex]x^2+10x+3=0[/tex]
Group terms containing x:
[tex]\begin{gathered} (x^2+10x+_{\text{ -}})+3-_{\text{ -}}=0 \\ \end{gathered}[/tex]
Take one half of the coefficient of x and square it:
[tex]\begin{gathered} (x^2+10+25)+3-25=0 \\ \end{gathered}[/tex]
The factors of 25 which sum to 10 are 5 and 5 so:
[tex]\begin{gathered} x^2+10+25=(x+5)(x+5)=(x+5)^2 \\ so\colon \\ (x+5)^2=22 \end{gathered}[/tex]
Answer:
[tex](x+5)^2=22[/tex]
