Question

How do you solve `x^2-3x = 28` by factoring?

Answer 1

`x=7,-4`

Explanation:

In order to use the zero product principle, we must have a polynomial equal to 0. This means we need to manipulate the equation we have so that it fits this form:

`x^2 - 3x - 28 = 0`

Subtracting the 28 from the right side should fit the form.

Now we can begin factoring. Two numbers that multiply to equal -28 can be -14 and 2, -7 and 4, -28 and 1, and possibly others. But we also need these two numbers to, when added, equal -3. -7 and 4 fit this description. This brings us to the equation:

`(x-7)(x+4)=0`

We can then set each part of the factored form equal to 0:

`x-7=0`
`x=7`
And:
`x+4=0`
`x=-4`

We then have our answer, `x=-4,7`

I hope this helped!