Solve f(x)=3x^2-7x+23,text{when}x=-2?

$$f ( x ) = 3 x ^ { 2 } - 7 x + 23 , \text { when } x = - 2 ?$$

Solve for f, x

$$x=-2$$

$$f = -\frac{49}{2} = -24\frac{1}{2} = -24.5$$

Solution Steps

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

$$f\left(-2\right)=3\left(-2\right)^{2}-7\left(-2\right)+23$$

Calculate -2 to the power of 2 and get 4.

$$f\left(-2\right)=3\times 4-7\left(-2\right)+23$$

Multiply 3 and 4 to get 12.

$$f\left(-2\right)=12-7\left(-2\right)+23$$

Multiply -7 and -2 to get 14.

$$f\left(-2\right)=12+14+23$$

Add 12 and 14 to get 26.

$$f\left(-2\right)=26+23$$

Add 26 and 23 to get 49.

$$f\left(-2\right)=49$$

Divide both sides by -2.

$$f=-\frac{49}{2}$$

The system is now solved.

$$f=-\frac{49}{2} x=-2$$