Solve {l}{F(x)=1/(x+2)^2}{x+2-2=1/2}

$$\left. \begin{array} { l } { F ( x ) = \frac { 1 } { ( x + 2 ) ^ { 2 } } } \\ { x + 2 - 2 = \frac { 1 } { 2 } } \end{array} \right.$$

Solve for F, x

$$x=\frac{1}{2}=0.5$$

$$F=\frac{8}{25}=0.32$$

Solution Steps

Consider the second equation. Subtract 2 from 2 to get 0.

$$x=\frac{1}{2}$$

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

$$F\times \frac{1}{2}=\frac{1}{\left(\frac{1}{2}+2\right)^{2}}$$

Add \frac{1}{2} and 2 to get \frac{5}{2}.

$$F\times \frac{1}{2}=\frac{1}{\left(\frac{5}{2}\right)^{2}}$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$F\times \frac{1}{2}=\frac{1}{\frac{25}{4}}$$

Divide 1 by \frac{25}{4} by multiplying 1 by the reciprocal of \frac{25}{4}.

$$F\times \frac{1}{2}=1\times \frac{4}{25}$$

Multiply 1 and \frac{4}{25} to get \frac{4}{25}.

$$F\times \frac{1}{2}=\frac{4}{25}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$F=\frac{4}{25}\times 2$$

Multiply \frac{4}{25} and 2 to get \frac{8}{25}.

$$F=\frac{8}{25}$$

The system is now solved.

$$F=\frac{8}{25} x=\frac{1}{2}$$