Question

What are the solutions to the equation 0 = x2 – x –6? Select two options

Answer 1

(X-3)(x+2)=0

So, X=3,X= -2
X={3,-2}

Answer 2

`x=3` or
`x=-2`

Explanation:

This is factorable.

The leading coefficient is 1.

Since this is a quadratic all we have to do is find two numbers that multiply to be c and add up to be b to factor the expression that is to the left of the equal sign.

By the way a quadratic expression looks like
`ax^2+bx+c`.

So we want to find two numbers that multiply to be -6 and add up to be -1.

Those numbers are -3 and 2 since (-3)(2)=-6 and -3+2=-1.

So the factored form is:

`(x-3)(x+2)=0`.

Since we have a product is zero then at least one of the factors need to be zero in order for the equation to hold.

So this means we have the following two equations to solve:

`x-3=0` or
`x+2=0`

First equation we will add 3 on both sides.

Second equation we will subtract 2 on both sides.

`x=3` or
`x=-2`