Solve x^2/2+x/18-1/30

$$\frac { x ^ { 2 } } { 2 } + \frac { x } { 18 } - \frac { 1 } { 30 }$$

Evaluate

$$\frac{x^{2}}{2}+\frac{x}{18}-\frac{1}{30}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 18 is 18. Multiply \frac{x^{2}}{2} times \frac{9}{9}.

$$\frac{9x^{2}}{18}+\frac{x}{18}-\frac{1}{30}$$

Since \frac{9x^{2}}{18} and \frac{x}{18} have the same denominator, add them by adding their numerators.

$$\frac{9x^{2}+x}{18}-\frac{1}{30}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 18 and 30 is 90. Multiply \frac{9x^{2}+x}{18} times \frac{5}{5}. Multiply \frac{1}{30} times \frac{3}{3}.

$$\frac{5\left(9x^{2}+x\right)}{90}-\frac{3}{90}$$

Since \frac{5\left(9x^{2}+x\right)}{90} and \frac{3}{90} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(9x^{2}+x\right)-3}{90}$$

Do the multiplications in 5\left(9x^{2}+x\right)-3.

$$\frac{45x^{2}+5x-3}{90}$$

Factor

$$\frac{\left(x-\left(-\frac{\sqrt{565}}{90}-\frac{1}{18}\right)\right)\left(x-\left(\frac{\sqrt{565}}{90}-\frac{1}{18}\right)\right)}{2}$$