Step 1
Given;
[tex]3x^2+18x+15=0[/tex]Required; To solve by completing the square method.
Step 2
Subtract 15 from both sides of the equation.
[tex]\begin{gathered} 3x^2+18x+15-15=0-15 \\ 3x^2+18x=-15 \end{gathered}[/tex][tex]\begin{gathered} Divide\text{ all terms by 3} \\ x^2+6x=-5 \end{gathered}[/tex]Find half of the coefficient of x (i.e 6) and square it
[tex](\frac{6}{2})^2=3^2[/tex]Add it to both sides
[tex]\begin{gathered} x^2+6x+3^2=-5+3^2 \\ Use\text{ perfect square} \\ (x+3)^2=-5+9 \\ (x+3)^2=4 \\ x+3=\pm\sqrt{4} \\ x=\operatorname{\pm}\sqrt{4}-3 \end{gathered}[/tex][tex]\begin{gathered} x=\pm2-3 \\ x=-1\text{ or -5} \end{gathered}[/tex]Answer;
[tex]x=-1,-5[/tex]