SOLUTION: Hi, I have an Algebra question. It is a word problem that I am supposed to state as a quadratic equation. I am to use one of 3 methods: factoring, completing the square, or the q

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Hi, I have an Algebra question. It is a word problem that I am supposed to state as a quadratic equation. I am to use one of 3 methods: factoring, completing the square, or the q      Log On


   

Question 711727: Hi,
I have an Algebra question. It is a word problem that I am supposed to state as a quadratic equation. I am to use one of 3 methods: factoring, completing the square, or the quadratic formula.
The problem is:
The difference of two positive numbers is six. Their product is 223 less than the sum of their squares. What are the two numbers?
Thanks
Amber
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
y-x=6 and xy=-223%2Bx%5E2%2By%5E2

Using the simpler equation, y=x+6. Substitute into the quadratic equation.
x%28x%2B6%29=-223%2Bx%5E2%2B%28x%2B6%29%5E2
x%5E2%2B6x=x%5E2%2B%28x%5E2%2B12x%2B36%29-223
x%5E2%2B6x=2x%5E2%2B12x-187
0=x%5E2%2B6x-187

Solution to quadratic formula makes the most sense because looking for several factorizations for 187 is not efficient in time. (Unless you just SEE IT).

Intentionally using the positive root,
x=%28-6%2Bsqrt%286%5E2-4%28-187%29%29%29%2F2 = 11, highlight%28x=11%29
Based on that and required difference, highlight%28y=17%29.