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

1 Answer
Oct 8, 2015

Answer:

#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!