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

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Answer 1 · 2015-08-22T07:26:47

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

$7r^2-14r=-7$

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

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

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

How do you solve 7r^2 - 14r= -77r^2 - 14r= -7 by factoring?