Solve {l}{-150^2+6a+2=0}{b=a}{text{Solvefor}ctext{where}}{c=b}

$$\left. \begin{array} { l } { -150 ^ {2} + 6 a + 2 = 0 }\\ { b = a }\\ { \text{Solve for } c \text{ where} } \\ { c = b } \end{array} \right.$$

Solve for a, b, c

$$c = \frac{11249}{3} = 3749\frac{2}{3} \approx 3749.666666667$$

Solution Steps

Consider the first equation. Calculate 150 to the power of 2 and get 22500.

$$-22500+6a+2=0$$

Add -22500 and 2 to get -22498.

$$-22498+6a=0$$

Add 22498 to both sides. Anything plus zero gives itself.

$$6a=22498$$

Divide both sides by 6.

$$a=\frac{22498}{6}$$

Reduce the fraction \frac{22498}{6} to lowest terms by extracting and canceling out 2.

$$a=\frac{11249}{3}$$

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

$$b=\frac{11249}{3}$$

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

$$c=\frac{11249}{3}$$

The system is now solved.

$$a=\frac{11249}{3} b=\frac{11249}{3} c=\frac{11249}{3}$$