Solve frac{4-(1-sqrt{14}+15/4)}{2}

$$\frac{ 4-(1- \sqrt{ 14 } + \frac{ 15 }{ 4 } ) }{ 2 }$$

Evaluate

$$\frac{\sqrt{14}}{2}-\frac{3}{8}\approx 1.495828693$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

$$\frac{4-\left(\frac{4}{4}-\sqrt{14}+\frac{15}{4}\right)}{2}$$

Since \frac{4}{4} and \frac{15}{4} have the same denominator, add them by adding their numerators.

$$\frac{4-\left(\frac{4+15}{4}-\sqrt{14}\right)}{2}$$

Add 4 and 15 to get 19.

$$\frac{4-\left(\frac{19}{4}-\sqrt{14}\right)}{2}$$

To find the opposite of \frac{19}{4}-\sqrt{14}, find the opposite of each term.

$$\frac{4-\frac{19}{4}-\left(-\sqrt{14}\right)}{2}$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{\frac{16}{4}-\frac{19}{4}-\left(-\sqrt{14}\right)}{2}$$

Since \frac{16}{4} and \frac{19}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16-19}{4}-\left(-\sqrt{14}\right)}{2}$$

Subtract 19 from 16 to get -3.

$$\frac{-\frac{3}{4}-\left(-\sqrt{14}\right)}{2}$$

The opposite of -\sqrt{14} is \sqrt{14}.

$$\frac{-\frac{3}{4}+\sqrt{14}}{2}$$

Factor

$$\frac{4 \sqrt{14} - 3}{8} = 1.4958286933869707$$