Answer: 8 = x or -7 = x
Step-by-step explanation: To solve this problem, let's translate the first sentence into an equation.
"A number" which we can represent as X "is" which means equals "56 less than its square" which is X² - 56.
Remember that the word "less than" switches the order around. In other words, 56 less than its square is not 56 - X² its X² - 56.
Next, since we have an X² term in our equation, we set it equal to 0 by subtracting X from both sides and we have the following equation.
0 = X² - X - 56
Next, we factor the right side as the product of two binomials. In the first position of each binomial, we have the factors of X² which are X and X. In the second position of each binomial, we are looking for the factors of -56 that add to -1 which are -8 and 7.
Now, we have the following equation.
0 = (x - 8) (x + 7)
This means that either 0 = x - 8 or 0 = x + 7.
Finally, in the first equation we add 8 to both sides to get 8 = X. In the second equation, we subtract 7 from both sides to get -7 = X.
It's important to understand that both of these answers work. If we plug in 8 back into the original problem, we have 8 is 56 less that 8² or we can represent it as (8) = (8)² - 56 which simplifies to 8 = 64 - 56 or 8 = 8 which is a true statement.
If we plug in -7 back into the original problem, we have -7 is 56 less than -7² or (-7) = (-7)² - 56 which simplifies to -7 = 49 - 56 or -7 = -7 which is also a true statement.
