Answer:
Missing term is 225/4
Step-by-step explanation:
[tex]x^2+15x+18=0[/tex]
First move +18 to the other side. Subtract 18 on both sides
[tex]x^2+15x=-18[/tex]
In completing the square method we take the half of coefficient of x and then square it
coefficient of x is 15
Half of 15 is [tex]\frac{15}{2}[/tex]
Square it [tex](\frac{15}{2})^2[/tex]
[tex]\frac{225}{4}[/tex]
Missing term is 225/4 that is required to form a square trinomial
Add it on both sides
[tex]x^2+15x+\frac{225}{4}=-18+\frac{225}{4}[/tex]
[tex]x^2+15x+\frac{225}{4}=\frac{-18*4}{1*4}+\frac{225}{4}[/tex]
[tex]x^2+15x+\frac{225}{4}=\frac{-72}{4}+\frac{225}{4}[/tex]
[tex]x^2+15x+\frac{225}{4}=\frac{153}{4}[/tex]
Now we write left hand side in square form
[tex](x+\frac{15}{2})^2=\frac{153}{4}[/tex]
Now we solve for x
Take square root on both sides
[tex](x+\frac{15}{2})^2=\sqrt{\frac{153}{4}}[/tex]
[tex](x+\frac{15}{2})=+-\frac{3\sqrt{17}}{2}[/tex]
Subtract 15/2 on both sides
[tex]x=+-\frac{3\sqrt{17}}{2}-\frac{15}{2}[/tex]
