Solve P(x)=3x^3-8x^2+8x-3text{for}x=2

$$P ( x ) = 3 x ^ { 3 } - 8 x ^ { 2 } + 8 x - 3 \text { for } x = 2$$

Solve for P, x

$$x=2$$

$$P = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

Solution Steps

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

$$P\times 2=3\times 2^{3}-8\times 2^{2}+8\times 2-3$$

Calculate 2 to the power of 3 and get 8.

$$P\times 2=3\times 8-8\times 2^{2}+8\times 2-3$$

Multiply 3 and 8 to get 24.

$$P\times 2=24-8\times 2^{2}+8\times 2-3$$

Calculate 2 to the power of 2 and get 4.

$$P\times 2=24-8\times 4+8\times 2-3$$

Multiply -8 and 4 to get -32.

$$P\times 2=24-32+8\times 2-3$$

Subtract 32 from 24 to get -8.

$$P\times 2=-8+8\times 2-3$$

Multiply 8 and 2 to get 16.

$$P\times 2=-8+16-3$$

Add -8 and 16 to get 8.

$$P\times 2=8-3$$

Subtract 3 from 8 to get 5.

$$P\times 2=5$$

Divide both sides by 2.

$$P=\frac{5}{2}$$

The system is now solved.

$$P=\frac{5}{2} x=2$$