SOLUTION: Hi, I am more of an older folk here so its not for homework. Actually it was a question asked to me and I have had a hard time to figure it out and its driving me nuts. I also w

Question 186422: Hi, I am more of an older folk here so its not for homework. Actually it was a question asked to me and I have had a hard time to figure it out and its driving me nuts. I also was trying to show someone that there are sites out there for help in which it does not cost you. I think its wonderful you offer this. Ok here it goes. What two numbers when added together equals -6 and what same two numbers when multiplied equals -12. I hope you can help so I can show my friend there are people out there quite kind like you. Thank you
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
"two numbers when added together equals -6 " translates to and

"same two numbers when multiplied equals -12" translates to

Start with the first equation

Subtract "x" from both sides.

Rearrange the terms.

--------------------------------------------

Move onto the second equation

Plug in

Distribute

Multiply

Multiply EVERY term by -1 to make the leading coefficient positive.

Subtract 12 from both sides.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

Break up the fraction.

Reduce.

or Break up the expression.

So the answers are or

which approximate to or (use a calculator to find the approximate values).

==========================================================

Answer:

So the numbers are roughly 1.583 and -7.583 (in either order)

Note: 1.583 + -7.583 = -6 and 1.583 * -7.583 = -12.003889 (which is very close)
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