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

Aug 22, 2015

The solution is color(blue)(r=1

Explanation:

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

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

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 $a {r}^{2} + b r + c$, we need to think of 2 numbers such that:

${N}_{1} \cdot {N}_{2} = a \cdot c = 7 \cdot 7 = 49$
and
${N}_{1} + {N}_{2} = b = - 14$

After trying out a few numbers we get ${N}_{1} = - 7$ and ${N}_{2} = - 7$
$- 7 \cdot - 7 = 49$, and $\left(- 7\right) + \left(- 7\right) = - 14$

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

$7 r \left(r - 1\right) - 7 \left(r - 1\right) = 0$

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