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

Question

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

1 Answer

Impact of this question

1349 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-16T17:03:31

The solutions is $x = - 3$ $color(blue)(x=-3$

Explanation:

$x^{2} + 6 x + 9 = 0$ $x^2+6x+9=0$

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

In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot 9 = 9$ $N_1*N_2 = a*c = 1*9 = 9$
AND
$N_{1} + N_{2} = b = 6$ $N_1 +N_2 = b = 6$
After trying out a few numbers we get $N_{1} = 3$ $N_1 = 3$ and $N_{2} = 3$ $N_2 =3$
$3 \cdot 3 = 9$ $3*3 = 9$ and $3 + 3 = 6$ $3+3= 6$

$x^{2} + 6 x + 9 = x^{2} + 3 x + 3 x + 9$ $x^2+6x+9=x^2+3x+3x+9$

$x (x + 3) + 3 (x + 3) = 0$ $x(x+3) +3(x+3)=0$

$(x + 3) (x + 3) = 0$ $(x+3)(x+3)=0$

Now we equate the factors to zero and find the solutions.
$x + 3 = 0, x = - 3$ $x+3 =0, color(blue)(x=-3$

$x + 3 = 0, x = - 3$ $x+3 =0, color(blue)(x=-3$

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve x^2+6x=-9x2+6x=−9x^2+6x=-9 by factoring?

1 Answer

Explanation:

Related questions

Impact of this question

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