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

Algebra ->  Equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
"two numbers when added together equals -6 " translates to x%2By=-6 and

"same two numbers when multiplied equals -12" translates to x%2Ay=-12


x%2By=-6 Start with the first equation


y=-6-x Subtract "x" from both sides.


y=-x-6 Rearrange the terms.


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x%2Ay=-12 Move onto the second equation


x%2A%28-x-6%29=-12 Plug in y=-x-6


x%2A%28-x%29-x%286%29=-12 Distribute


-x%5E2-6x=-12 Multiply


x%5E2%2B6x=12 Multiply EVERY term by -1 to make the leading coefficient positive.


x%5E2%2B6x-12=0 Subtract 12 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=6, and c=-12


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Plug in a=1, b=6, and c=-12


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36--48+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-12%29 to get -48


x+=+%28-6+%2B-+sqrt%28+36%2B48+%29%29%2F%282%281%29%29 Rewrite sqrt%2836--48%29 as sqrt%2836%2B48%29


x+=+%28-6+%2B-+sqrt%28+84+%29%29%2F%282%281%29%29 Add 36 to 48 to get 84


x+=+%28-6+%2B-+sqrt%28+84+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+2%2Asqrt%2821%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-6%29%2F%282%29+%2B-+%282%2Asqrt%2821%29%29%2F%282%29 Break up the fraction.


x+=+-3+%2B-+sqrt%2821%29 Reduce.


x+=+-3%2Bsqrt%2821%29 or x+=+-3-sqrt%2821%29 Break up the expression.


So the answers are x+=+-3%2Bsqrt%2821%29 or x+=+-3-sqrt%2821%29


which approximate to x=1.583 or x=-7.583 (use a calculator to find the approximate values).


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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)