Solve {l}{f(x)=4x^6-16x^3+7x^2+20}{text{a.}quadx=5text{and}}

$$\left. \begin{array} { l } { f ( x ) = 4 x ^ { 6 } - 16 x ^ { 3 } + 7 x ^ { 2 } + 20 } \\ { \text { a. } \quad x = 5 \text { and } } \end{array} \right.$$

Solve for f, x

$$x=5$$

$$f=12139$$

Solution Steps

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

$$f\times 5=4\times 5^{6}-16\times 5^{3}+7\times 5^{2}+20$$

Calculate 5 to the power of 6 and get 15625.

$$f\times 5=4\times 15625-16\times 5^{3}+7\times 5^{2}+20$$

Multiply 4 and 15625 to get 62500.

$$f\times 5=62500-16\times 5^{3}+7\times 5^{2}+20$$

Calculate 5 to the power of 3 and get 125.

$$f\times 5=62500-16\times 125+7\times 5^{2}+20$$

Multiply -16 and 125 to get -2000.

$$f\times 5=62500-2000+7\times 5^{2}+20$$

Subtract 2000 from 62500 to get 60500.

$$f\times 5=60500+7\times 5^{2}+20$$

Calculate 5 to the power of 2 and get 25.

$$f\times 5=60500+7\times 25+20$$

Multiply 7 and 25 to get 175.

$$f\times 5=60500+175+20$$

Add 60500 and 175 to get 60675.

$$f\times 5=60675+20$$

Add 60675 and 20 to get 60695.

$$f\times 5=60695$$

Divide both sides by 5.

$$f=\frac{60695}{5}$$

Divide 60695 by 5 to get 12139.

$$f=12139$$

The system is now solved.

$$f=12139 x=5$$