SOLUTION: x^2+6x-6=6, then x=?

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Question 507675: x^2+6x-6=6, then x=?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B6x-6=6 Start with the given equation.


x%5E2%2B6x-6-6=0 Get every term to the left side.


x%5E2%2B6x-12=0 Combine like terms.


Notice that the quadratic x%5E2%2B6x-12 is 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 solutions are x+=+-3%2Bsqrt%2821%29 or x+=+-3-sqrt%2821%29

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim