Solve -x/3+7/2+x^2

$$- \frac { x } { 3 } + \frac { 7 } { 2 } + x ^ { 2 }$$

Evaluate

$$x^{2}-\frac{x}{3}+\frac{7}{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 2 is 6. Multiply -\frac{x}{3} times \frac{2}{2}. Multiply \frac{7}{2} times \frac{3}{3}.

$$-\frac{2x}{6}+\frac{7\times 3}{6}+x^{2}$$

Since -\frac{2x}{6} and \frac{7\times 3}{6} have the same denominator, add them by adding their numerators.

$$\frac{-2x+7\times 3}{6}+x^{2}$$

Do the multiplications in -2x+7\times 3.

$$\frac{-2x+21}{6}+x^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2} times \frac{6}{6}.

$$\frac{-2x+21}{6}+\frac{6x^{2}}{6}$$

Since \frac{-2x+21}{6} and \frac{6x^{2}}{6} have the same denominator, add them by adding their numerators.

$$\frac{-2x+21+6x^{2}}{6}$$

Factor

$$\frac{6x^{2}-2x+21}{6}$$

Solution Steps

Factor out \frac{1}{6}. Polynomial -2x+21+6x^{2} is not factored since it does not have any rational roots.

$$\frac{-2x+21+6x^{2}}{6}$$