How do you solve #7r^2 - 14r= -7# by factoring?

1 Answer
Aug 22, 2015

Answer:

The solution is #color(blue)(r=1#

Explanation:

#7r^2-14r=-7#

#7r^2-14r+7=0#

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like #ar^2 + br + c#, we need to think of 2 numbers such that:

#N_1*N_2 = a*c = 7*7 =49#
and
#N_1 +N_2 = b = -14#

After trying out a few numbers we get #N_1 = -7# and #N_2 =-7#
#-7*-7 = 49#, and #(-7)+(-7)= -14#

#7r^2-14r+7=7r^2-7r-7r+7#
#7r^2-7r-7r+7=0#

#7r(r-1) -7(r-1)=0#

#color(blue)((7r-7)(r-1)=0#

We now equate these factors to zero

#7r-7=0, color(blue)(r=1#
#r-1=0, color(blue)(r=1#