Can anyone solve this Pre-Calculus question please?

Question

Find the sales necessary to break even (R = C) if the cost C of producing x units and the revenue R for selling x units are given by the following equations.

C = 5.5√x + 13,000

R = 3.81x

x=? units

R=C=?

my best answers are 620, but it's wrong.

Answer 1

Since R = C, equate the two:

3.81x = 5.5√x + 13,000

Rearrange:

3.81x - 13,000 = 5.5√x

Square both sides (doing the actual calculations later):

3.81² x² - (2 * 3.81 * 13,000) x + 13,000² = 5.5² x

Rearrange again:

3.81² x² - (2 * 3.81 * 13,000 - 5.5²) x + 13,000² = 0

Now solve the quadratic using the quadratic formula, letting a = 3.81², b = - (2 * 3.81 * 13,000 - 5.5²), and c = 13,000². (I'm assuming you know the quadratic formula). There are two roots, x = 3497.45 and x = 3328.79. Which is correct? The only way to tell is to resubstitute into the original equations. If x = 3328.79, then R = 12,682.67 and C = 13,317.33. Since these are not equal, then x = 3328.79 is incorrect. If x = 3497.45, then R = C = 13,325.27. Therefore x = 3497.45 is the correct answer.