Question

Solve the equation by factoring: x^2 + 13x = -42

Answer 1

x^2+13x=-42
x^2+13x+42=0
(x+6)(x+7)=0
X=-6,-7

Answer 2

-6 and -7 are the roots

Explanation:

The quadratic equation given is:

`x^(2)+13x=-42\\Taking\ -42\ to\ left\ hand\ side\ we\ get\\x^(2) +13x+42=0`

We can factorise the equation as:

`x^(2)+6x+7x+42=0\\(x^(2)+6x)+(7x+42)=0\\`

Taking x common from the first bracket and 7 common from the second bracket we get:

`x(x+6)+7(x+6)`

Taking (x+6) common from both terms we get:

`(x+6)(x+7)=0`

x= -6 or x=-7

Hence -6 and -7 are the roots of the given quadratic equation.