Solve f(x)=5x^3+4x^2+8x+1text{when}x=2

$$f ( x ) = 5 x ^ { 3 } + 4 x ^ { 2 } + 8 x + 1 \text { when } x = 2$$

Solve for f, x

$$x=2$$

$$f = \frac{73}{2} = 36\frac{1}{2} = 36.5$$

Solution Steps

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

$$f\times 2=5\times 2^{3}+4\times 2^{2}+8\times 2+1$$

Calculate 2 to the power of 3 and get 8.

$$f\times 2=5\times 8+4\times 2^{2}+8\times 2+1$$

Multiply 5 and 8 to get 40.

$$f\times 2=40+4\times 2^{2}+8\times 2+1$$

Calculate 2 to the power of 2 and get 4.

$$f\times 2=40+4\times 4+8\times 2+1$$

Multiply 4 and 4 to get 16.

$$f\times 2=40+16+8\times 2+1$$

Add 40 and 16 to get 56.

$$f\times 2=56+8\times 2+1$$

Multiply 8 and 2 to get 16.

$$f\times 2=56+16+1$$

Add 56 and 16 to get 72.

$$f\times 2=72+1$$

Add 72 and 1 to get 73.

$$f\times 2=73$$

Divide both sides by 2.

$$f=\frac{73}{2}$$

The system is now solved.

$$f=\frac{73}{2} x=2$$