Quadratic Formula: Finding Solutions for a Quadratic Equation

[stevecallaway]

Homework Statement

.002x - .000001x^2 = .50

Homework Equations

-b+-sq.rt.((b^2)-(4ac))/2a



3. The Attempt at a Solution
Plugging a=-.000001, b=.002, and c=-.5 does not get the the correct answer. x is supposed to be 292.89. I can't remember any other way of going about trying to get this answer. Any suggestions?

 

[elibj123]

The formula is

( -b +- sqrt(b^2-4ac))/(2a)

 

[Mentallic]

As elibj123 said, the quadratic formula has a $\pm$ to consider. There are two solutions to any quadratic.

So you need to solve $$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

You'll get your solution of 292.89 if you take $$x=\frac{-b-\sqrt{b^2-4ac}}{2a}$$

but you'll also get a solution of approx 1700 if you solve $$x=\frac{-b+\sqrt{b^2-4ac}}{2a}$$

Both solutions are correct, and you can check this by substituting your values of x back into the original equation .002x - .000001x^2 = .50
If your values of x are correct, the Left-hand side should approximately equal the right-hand side (depending on the approximation of your values of x).