Answer:
The numbers are 14 and 16.
Explanation:
Equation:
x (x - 2) = 224
Solution:
x (x - 2) = 224
x² - 2x = 224
x² - 2x - 224 = 0
Now, we ended up with a trinomial. To find the two numbers, we need to factor it.
Factoring Trinomials
Trinomial is a polynomial with three terms which are connected by plus or minus notations. It is expressed as a² + b + c.
To factor, we need to follow these steps:
1. Find the factors of "ac" that when combined it will result to "b".
2. When "c" is positive, the sign in each binomial is the same as "b".
3. When "c" is negative, the sign in each binomial is different.
4. Write as the product of two binomials ( )( ).
Let us continue.
x² - 2x - 224
(x - 16)(x + 14)
Therefore, x = 16 and x = -14.
Since we are looking for a positive value, we are going to use the positive value of x and that is 16.
Larger number is 16.
x - 2 = 16 - 2 = 14
Smaller number is 14.
Final Answer:
The two numbers are 14 and 16.
Checking:
x (x - 2) = 224
16 (16 - 2) = 224
16 (14) = 224
224 = 224 ✔