Solve {c}{f(x)=2*(200-x)^2/x^3-1/2x-600}{x=350.08}

$$\left. \begin{array} { c } { f ( x ) = \frac { 2 \cdot ( 200 - x ) ^ { 2 } } { x ^ { 3 } } - \frac { 1 } { 2 } x - 600 } \\ { x = 350.08 } \end{array} \right.$$

Solve for f, x

$$x=350.08$$

$$f = -\frac{101478840138711}{45837325148672} = -2\frac{9804189841367}{45837325148672} \approx -2.213890968$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$f\times 350.08=\frac{2\left(200-350.08\right)^{2}}{350.08^{3}}-\frac{1}{2}\times 350.08-600$$

Subtract 350.08 from 200 to get -150.08.

$$f\times 350.08=\frac{2\left(-150.08\right)^{2}}{350.08^{3}}-\frac{1}{2}\times 350.08-600$$

Calculate -150.08 to the power of 2 and get 22524.0064.

$$f\times 350.08=\frac{2\times 22524.0064}{350.08^{3}}-\frac{1}{2}\times 350.08-600$$

Multiply 2 and 22524.0064 to get 45048.0128.

$$f\times 350.08=\frac{45048.0128}{350.08^{3}}-\frac{1}{2}\times 350.08-600$$

Calculate 350.08 to the power of 3 and get 42904406.720512.

$$f\times 350.08=\frac{45048.0128}{42904406.720512}-\frac{1}{2}\times 350.08-600$$

Expand \frac{45048.0128}{42904406.720512} by multiplying both numerator and the denominator by 1000000.

$$f\times 350.08=\frac{45048012800}{42904406720512}-\frac{1}{2}\times 350.08-600$$

Reduce the fraction \frac{45048012800}{42904406720512} to lowest terms by extracting and canceling out 8192.

$$f\times 350.08=\frac{5499025}{5237354336}-\frac{1}{2}\times 350.08-600$$

Multiply -\frac{1}{2} and 350.08 to get -\frac{4376}{25}.

$$f\times 350.08=\frac{5499025}{5237354336}-\frac{4376}{25}-600$$

Subtract \frac{4376}{25} from \frac{5499025}{5237354336} to get -\frac{22918525098711}{130933858400}.

$$f\times 350.08=-\frac{22918525098711}{130933858400}-600$$

Subtract 600 from -\frac{22918525098711}{130933858400} to get -\frac{101478840138711}{130933858400}.

$$f\times 350.08=-\frac{101478840138711}{130933858400}$$

Divide both sides by 350.08.

$$f=\frac{-\frac{101478840138711}{130933858400}}{350.08}$$

Express \frac{-\frac{101478840138711}{130933858400}}{350.08} as a single fraction.

$$f=\frac{-101478840138711}{130933858400\times 350.08}$$

Multiply 130933858400 and 350.08 to get 45837325148672.

$$f=\frac{-101478840138711}{45837325148672}$$

Fraction \frac{-101478840138711}{45837325148672} can be rewritten as -\frac{101478840138711}{45837325148672} by extracting the negative sign.

$$f=-\frac{101478840138711}{45837325148672}$$

The system is now solved.

$$f=-\frac{101478840138711}{45837325148672} x=350.08$$