Solve {l}{f{(-10)}=3(-10)^3+4(-10)^2}{text{Solvefor}gtext{where}}{g=-3{(-10)}+7}

$$\left. \begin{array} { l } { f {(-10)} = 3 {(-10)} ^ {3} + 4 {(-10)} ^ {2} }\\ { \text{Solve for } g \text{ where} } \\ { g = -3 {(-10)} + 7 } \end{array} \right.$$

Solve for f, g

$$g=37$$

Solution Steps

Consider the first equation. Calculate -10 to the power of 3 and get -1000.

$$f\left(-10\right)=3\left(-1000\right)+4\left(-10\right)^{2}$$

Multiply 3 and -1000 to get -3000.

$$f\left(-10\right)=-3000+4\left(-10\right)^{2}$$

Calculate -10 to the power of 2 and get 100.

$$f\left(-10\right)=-3000+4\times 100$$

Multiply 4 and 100 to get 400.

$$f\left(-10\right)=-3000+400$$

Add -3000 and 400 to get -2600.

$$f\left(-10\right)=-2600$$

Divide both sides by -10.

$$f=\frac{-2600}{-10}$$

Divide -2600 by -10 to get 260.

$$f=260$$

Consider the second equation. Multiply -3 and -10 to get 30.

$$g=30+7$$

Add 30 and 7 to get 37.

$$g=37$$

The system is now solved.

$$f=260 g=37$$