How do you solve $x^2+6x+2=9$ by factoring?

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Answer 1 · 2015-08-16T17:00:43

The solutions are:

$color(blue)(x=1$
$color(blue)(x=-7$

$x^2+6x+2=9$
$x^2+6x+2-9=0$
$x^2+6x-7=0$

We can Split the Middle Term of this expression to factorise it and then we find the 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:

$N_1*N_2 = a*c = 1*-7 = -7$
and
$N_1 +N_2 = b = 6$

After trying out a few numbers we get $N_1 = 7$ and $N_2 =-1$
$7*(-1) = -7$ , and $7+(-1)= 6$

$x^2+6x-7 = x^2+7x-1x-7$
$x(x+7)(-1(x+7)=0$
$(x-1)(x+7)=0$
Now we equate the factors to zero and find the solutions.

$x-1=0,color(blue)(x=1$
$x+7=0,color(blue)(x=-7$

How do you solve x^2+6x+2=9x^2+6x+2=9 by factoring?