Solve P(b)=6b^2+8b-8;b=6

$$P ( b ) = 6 b ^ { 2 } + 8 b - 8 ; b = 6$$

Solve for P, b

$$P = \frac{128}{3} = 42\frac{2}{3} \approx 42.666666667$$

$$b=6$$

Solution Steps

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

$$P\times 6=6\times 6^{2}+8\times 6-8$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$P\times 6=6^{3}+8\times 6-8$$

Calculate 6 to the power of 3 and get 216.

$$P\times 6=216+8\times 6-8$$

Multiply 8 and 6 to get 48.

$$P\times 6=216+48-8$$

Add 216 and 48 to get 264.

$$P\times 6=264-8$$

Subtract 8 from 264 to get 256.

$$P\times 6=256$$

Divide both sides by 6.

$$P=\frac{256}{6}$$

Reduce the fraction \frac{256}{6} to lowest terms by extracting and canceling out 2.

$$P=\frac{128}{3}$$

The system is now solved.

$$P=\frac{128}{3} b=6$$