How do you solve #-3x^2+7x= -5# by completing the square?

1 Answer
Jun 24, 2018

Answer:

#x=(7+-sqrt109)/6#

Explanation:

You should always start by what you want to reach, namely an expression on the form of
#(x-a)^2=b#
But first, to get some idea, let's start with a graph of the function
#f(x)= -3x^2+7x+5#:
enter image source here

We want #(x-a)^2=x^2-2ax+a^2# on the left side
Our expression has
#-3x^x+7x=-5#
Let's simplify by dividing the whole on #-3#:
#x^2-7/3x=5/3#

Therefore #-2ax=-7/3x# or #2a=7/3#, #a=7/6#
Add #a^2=(7/6)^2# on both sides:
#x^2-7/3x+(7/6)^2=5/3+49/6^2#
#(x-7/6)^2=(5*12+49)/6^2=109/6^2#
#x-7/6=+-sqrt109/6#
#x=(7+-sqrt109)/6#