Question

3x^2-18x + 225 = 0put equation in (x+a)^2=b form.

Answer 1

`3x^2-18x+225=0`

To put an equation as the given in the form (x+a)^2=b you need to complete the square:

You factorize the equation, as follow:

`3x^2-18x+225=3(x^2-6x+75)`

Then, you have that:

You have the equation in form:

`x^2+2ax+a^2`

You can identify the 2a as -6:

`2a=-6`

Then, a will be:

`a=-(6)/(2)=-3`

You add and substract a^2:

`3(x^2-6x+75+(-3)^2-(-3)^2)`

As:

`x^2+2ax+a^2=(x+a)^2`

You organize the equation as follow:

`=3(x^2-6x+(-3)^2+75-(-3)^2)`

Then, you get that:

`x^2-6x+(-3)^2=(x-3)^2`

Now you complete the square:

`3((x-3)^2+75-(-3)^2)=0`

You simplify:

`3((x-3)^2+75-9)=0`
`3((x-3)^2+66)=0`

You divide both sides of the equation into 3:

`(x-3)^2+66=0`

You substract 66 in both sides of the equation:

`(x-3)^2=-66`Then, the given equation is equal to (x-3)^2=-66