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the square of a number plus the number is 72

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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 (x2)

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

Now we have x2+x=72.

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


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


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