Solving y = 4x - x^2 for x

[charly_w]

Please help with solving for x: y=4x-x^2

 

[Mrspi]

Re: Solving for x

Please help with solving for x: y=4x-x^2

You can complete the square in x.

y = -x[sup:109bbdy3]2[/sup:109bbdy3] + 4x

I'd multiply both sides by -1, so you have a positive coefficient on the x^2 term:

-y = x[sup:109bbdy3]2[/sup:109bbdy3] - 4x

To make a perfect square trinomial out of what is on the right side, take HALF the coefficient of the x term, and square it. Half of 4 is 2, and 2[sup:109bbdy3]2[/sup:109bbdy3] is 4. So, you'll need to ADD 4 to the right side...which means you must also add 4 to the left side:

-y + 4 = x[sup:109bbdy3]2[/sup:109bbdy3] - 4x + 4

Rewrite the right side as the square of a binomial:

-y + 4 = (x - 2)[sup:109bbdy3]2[/sup:109bbdy3]

And take the square root of both sides:

+ sqrt(-y + 4) = x - 2

2 + sqrt(-y + 4) = x

 

[Denis]

Re: Solving for x

Or use quadratic equation:

y = 4x - x^2
x^2 - 4x + y = 0

x = 4 +- ....... finish it