the square of a number plus the number is 72

Hi Caity!

Let's break this down and set up an equation:

The square of a number-let's call this number x, so the square of x is x squared (x^{2})

Then it says plus the number, still x, so +x

Now we have x^{2}+x=72.

To solve this we need to make the equation equal to zero, so move the 72 over by subtracting from both sides.

x^{2}+x-72=0

Now we factor. Factoring can be tricky, we need two numbers that when multiplied equal -72 and subtracted equal one. SO one is positive and one is negative.

(x+ )(x- )

there are many factors of 72:

1*72, 2*36, 3*42, 4*18, 6*12, 8*9

The only ones that subtract to equal one would be 8*9

(x+9)(x-8)

Then check your work by FOIL to make sure it's correct!