How do you solve $x^2 + 9x + 8 = 0$ by factoring?

Question

28080 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-20T13:07:54

The solutions are
$color(blue)( x=-1$
$color(blue)(x=-8$

$x^2+9x+8=0$

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 $ax^2 + bx+ c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c =1*8 =8$
and
$N_1 +N_2 = b = 9$

After trying out a few numbers we get $N_1 = 8$ and $N_2=1$

$8*1 = 8$ , and $8+ 1= 9$

$x^2+9x+8=x^2+8x+1x+8$

$x(x+8) +1(x+8)=0$

$color(blue)((x+1)(x+8))=0$ is the factorised form of the equation.

Now we equate the factors to the R.H.S(0)
$x+1=0,color(blue)( x=-1$
$x+8=0, color(blue)(x=-8$

How do you solve x^2 + 9x + 8 = 0 x^2 + 9x + 8 = 0 by factoring?