SOLUTION: Please solve the equation y=x^2+4x-6 for the variable x. I have tried to find the x values where y is equal to "0" and although these two are related, they are not the same problem

Algebra ->  Expressions-with-variables -> SOLUTION: Please solve the equation y=x^2+4x-6 for the variable x. I have tried to find the x values where y is equal to "0" and although these two are related, they are not the same problem      Log On


   

Question 842683: Please solve the equation y=x^2+4x-6 for the variable x. I have tried to find the x values where y is equal to "0" and although these two are related, they are not the same problem. I am trying to figure out how x depends on y. What is throwing me off is the x^2. I know that I have to isolate x. I have tried using the quadratic equation formula but the answers I received were wrong (x=-2+sqrt10 and x=-2-sqrt10). Any help would be appreciated. Thank you in advance.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Treat y as a constant. You can then either complete the square to find formulas for x, or you can directly use the general solution to a quadratic equation.

Again, if y is a constant, then x%5E2%2B4x-6-y=0
x%5E2%2B4x-%28y%2B6%29=0.
Use Completion of Square if you want, but if you know the general solution process using it, then you know how to use the result for x.

highlight%28x=%28-4%2B-+sqrt%2816%2B4%28y%2B6%29%29%29%2F2%29 ----- I condensed a couple of steps there.
x=-2%2B-+sqrt%284%2By%2B6%29
highlight%28highlight%28x=-2%2B-+sqrt%28y%2B10%29%29%29 ---- most simplified