Solve {l}{(x)=f(x)=1/sqrt{2pi5}e^-frac{1{50}(x-50)^2}}{text{(1)}P(xleq45)text{(2)}P(xgeq55)}

$$\left. \begin{array} { l } { ( x ) = f ( x ) = \frac { 1 } { \sqrt { 2 \pi } 5 } e ^ { - \frac { 1 } { 50 } ( x - 50 ) ^ { 2 } } } \\ { \text { (1) } P ( x \leq 45 ) \text { (2) } P ( x \geq 55 ) } \end{array} \right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&f=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract fx from both sides.

$$x-fx=0$$

Combine all terms containing x.

$$\left(1-f\right)x=0$$

Divide 0 by 1-f.

$$x=0$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&f=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract fx from both sides.

$$x-fx=0$$

Combine all terms containing x.

$$\left(1-f\right)x=0$$

Divide 0 by 1-f.

$$x=0$$