Question

By completing the square. What is the missing term required to form a square trinomial?

Answer 1

Answer:

Missing term is 225/4

Step-by-step explanation:

$x^2+15x+18=0$

First move +18 to the other side. Subtract 18 on both sides

$x^2+15x=-18$

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 $\frac{15}{2}$

Square it  $(\frac{15}{2})^2$

$\frac{225}{4}$

Missing term is 225/4 that is required to form a square trinomial

Add it on both sides

$x^2+15x+\frac{225}{4}=-18+\frac{225}{4}$

$x^2+15x+\frac{225}{4}=\frac{-18*4}{1*4}+\frac{225}{4}$

$x^2+15x+\frac{225}{4}=\frac{-72}{4}+\frac{225}{4}$

$x^2+15x+\frac{225}{4}=\frac{153}{4}$

Now we write left hand side in square form

$(x+\frac{15}{2})^2=\frac{153}{4}$

Now we solve for x

Take square root on both sides

$(x+\frac{15}{2})^2=\sqrt{\frac{153}{4}}$

$(x+\frac{15}{2})=+-\frac{3\sqrt{17}}{2}$

Subtract 15/2 on both sides

$x=+-\frac{3\sqrt{17}}{2}-\frac{15}{2}$