# How do you solve using completing the square method #-3x^2+30x-74#?

##### 2 Answers

This cannot really be "solved" because it is not an equation and it is not "equal" to anything. It can only be written in a different form.

I got:

#y = -3(x - 5)^2 + 1#

You have:

#y = -3x^2 + 30x - 74#

What you can start with is to make the **perfect-square** coefficient (

Then, **halve** the **square it**, adding it to both sides.

#y/3 = -x^2 + 10x - 74/3# (divide by 3)

#-y/3 = x^2 - 10x + 74/3# (switch signs)

Half of

#=> -y/3 + 75/3 = x^2 - 10x + 74/3 + 75/3#

#=> -y/3 = x^2 - 10x + 75/3 - 1/3#

#=> -y/3 = color(green)(x^2 - 10x + 25) - 1/3#

#=> -y/3 = color(green)((x - 5)^2) - 1/3#

Now you can return it back to

#=> y/3 = -(x - 5)^2 + 1/3#

#=> color(blue)(y = -3(x - 5)^2 + 1)#