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:

$a=-\frac{6}{2}=-3$

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