Solve {left(frac{sqrt{13}-1}{2}right)}^2-(frac{-sqrt{13}}{2})+2019

$${ \left( \frac{ \sqrt{ 13 } -1 }{ 2 } \right) }^{ 2 } -( \frac{ - \sqrt{ 13 } }{ 2 } )+2019$$

Evaluate

$$\frac{4045}{2}=2022.5$$

Short Solution Steps

To raise \frac{\sqrt{13}-1}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\sqrt{13}-1\right)^{2}}{2^{2}}-\frac{-\sqrt{13}}{2}+2019$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2^{2} and 2 is 4. Multiply \frac{-\sqrt{13}}{2} times \frac{2}{2}.

$$\frac{\left(\sqrt{13}-1\right)^{2}}{4}-\frac{2\left(-\sqrt{13}\right)}{4}+2019$$

Since \frac{\left(\sqrt{13}-1\right)^{2}}{4} and \frac{2\left(-\sqrt{13}\right)}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(\sqrt{13}-1\right)^{2}-2\left(-\sqrt{13}\right)}{4}+2019$$

Do the multiplications in \left(\sqrt{13}-1\right)^{2}-2\left(-\sqrt{13}\right).

$$\frac{\left(\sqrt{13}\right)^{2}-2\sqrt{13}+1+2\sqrt{13}}{4}+2019$$

Do the calculations in \left(\sqrt{13}\right)^{2}-2\sqrt{13}+1+2\sqrt{13}.

$$\frac{14}{4}+2019$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2019 times \frac{4}{4}.

$$\frac{14}{4}+\frac{2019\times 4}{4}$$

Since \frac{14}{4} and \frac{2019\times 4}{4} have the same denominator, add them by adding their numerators.

$$\frac{14+2019\times 4}{4}$$

Do the multiplications in 14+2019\times 4.

$$\frac{14+8076}{4}$$

Do the calculations in 14+8076.

$$\frac{8090}{4}$$

Reduce the fraction \frac{8090}{4} to lowest terms by extracting and canceling out 2.

$$\frac{4045}{2}$$

Factor

$$\frac{5 \cdot 809}{2} = 2022\frac{1}{2} = 2022.5$$