Solve P(x)=x^3-4/3x^2+5/2x-1,text{para}x=5

$$P ( x ) = x ^ { 3 } - \frac { 4 } { 3 } x ^ { 2 } + \frac { 5 } { 2 } x - 1 , \text { para } x = 5$$

Solve for P, x

$$x=5$$

$$P = \frac{619}{30} = 20\frac{19}{30} \approx 20.633333333$$

Solution Steps

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

$$P\times 5=5^{3}-\frac{4}{3}\times 5^{2}+\frac{5}{2}\times 5-1$$

Calculate 5 to the power of 3 and get 125.

$$P\times 5=125-\frac{4}{3}\times 5^{2}+\frac{5}{2}\times 5-1$$

Calculate 5 to the power of 2 and get 25.

$$P\times 5=125-\frac{4}{3}\times 25+\frac{5}{2}\times 5-1$$

Multiply -\frac{4}{3} and 25 to get -\frac{100}{3}.

$$P\times 5=125-\frac{100}{3}+\frac{5}{2}\times 5-1$$

Subtract \frac{100}{3} from 125 to get \frac{275}{3}.

$$P\times 5=\frac{275}{3}+\frac{5}{2}\times 5-1$$

Multiply \frac{5}{2} and 5 to get \frac{25}{2}.

$$P\times 5=\frac{275}{3}+\frac{25}{2}-1$$

Add \frac{275}{3} and \frac{25}{2} to get \frac{625}{6}.

$$P\times 5=\frac{625}{6}-1$$

Subtract 1 from \frac{625}{6} to get \frac{619}{6}.

$$P\times 5=\frac{619}{6}$$

Divide both sides by 5.

$$P=\frac{\frac{619}{6}}{5}$$

Express \frac{\frac{619}{6}}{5} as a single fraction.

$$P=\frac{619}{6\times 5}$$

Multiply 6 and 5 to get 30.

$$P=\frac{619}{30}$$

The system is now solved.

$$P=\frac{619}{30} x=5$$