Solve {l}{f(x)=-x^2+3x+5}{x=-3/5}

$$\left. \begin{array} { l } { f ( x ) = - x ^ { 2 } + 3 x + 5 } \\ { x = - \frac { 3 } { 5 } } \end{array} \right.$$

Solve for f, x

$$x=-\frac{3}{5}=-0.6$$

$$f = -\frac{71}{15} = -4\frac{11}{15} \approx -4.733333333$$

Solution Steps

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

$$f\left(-\frac{3}{5}\right)=-\left(-\frac{3}{5}\right)^{2}+3\left(-\frac{3}{5}\right)+5$$

Calculate -\frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$f\left(-\frac{3}{5}\right)=-\frac{9}{25}+3\left(-\frac{3}{5}\right)+5$$

Multiply 3 and -\frac{3}{5} to get -\frac{9}{5}.

$$f\left(-\frac{3}{5}\right)=-\frac{9}{25}-\frac{9}{5}+5$$

Subtract \frac{9}{5} from -\frac{9}{25} to get -\frac{54}{25}.

$$f\left(-\frac{3}{5}\right)=-\frac{54}{25}+5$$

Add -\frac{54}{25} and 5 to get \frac{71}{25}.

$$f\left(-\frac{3}{5}\right)=\frac{71}{25}$$

Multiply both sides by -\frac{5}{3}, the reciprocal of -\frac{3}{5}.

$$f=\frac{71}{25}\left(-\frac{5}{3}\right)$$

Multiply \frac{71}{25} and -\frac{5}{3} to get -\frac{71}{15}.

$$f=-\frac{71}{15}$$

The system is now solved.

$$f=-\frac{71}{15} x=-\frac{3}{5}$$