The answer is -6.
The word is indicates the equals sign, and less than indicates subtraction. So the problem can be rewritten like this:
a number = its square – 42 or x = x² – 42
So you have a regular number, a variable, and that same variable squared. Hopefully, these numbers ring a bell. With just a little rearranging, you have a quadratic equation!
x² – 42 = x
Now, just subtract x from both sides, and you're left with this:
x² – x – 42 = 0
There are numerous ways to solve for a quadratic equation. The simplest way is probably solving by factoring. You need to find two numbers whose product is -42 and whose sum is –1 (because –x is really –1x):
(x - 7) (x + 6) = 0
Use the FOIL method (First, Outer, Inner, Last) to multiply the two elements together and see if you get back to where you started. It looks like this:
First: x x x = x²
Outer: x x 6 = 6x
Inner: –7 x x = –7x
Last: –7 x 6 = –42
Add all those together and you get x² + 6x – 7x – 42, or x² –(1)x – 42 = 0, right back where you started!
In order for (x – 7)(x + 6) to equal 0, one of the elements — either (x – 7) or (x + 6) — must equal zero. Set each of these equal to 0 and you'll have your answer:
If x – 7 = 0, then x = 7
If x + 6 = 0, then x = –6
Now plug these answers into your original equation, x = x² – 42, to check your answers:
(7) = (7)² – 42
(–6) = (–6)² – 42
Parents are bombarded with messages to read with their children, but it’s rare to hear about the importance of doing math with them. Here are some helpful tips on why and how to instill a love of math in your children shared by pbs.org.