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

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

Solve for f, x

$$x = -\frac{5}{3} = -1\frac{2}{3} \approx -1.666666667$$

$$f = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Solution Steps

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

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

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

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

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

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

Subtract 5 from -\frac{25}{9} to get -\frac{70}{9}.

$$f\left(-\frac{5}{3}\right)=-\frac{70}{9}+5$$

Add -\frac{70}{9} and 5 to get -\frac{25}{9}.

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

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

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

Multiply -\frac{25}{9} and -\frac{3}{5} to get \frac{5}{3}.

$$f=\frac{5}{3}$$

The system is now solved.

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