Solve (frac{1+sqrt{385}}{3}-5)^2+75

$$( \frac { 1 + \sqrt { 385 } } { 3 } - 5 ) ^ { 2 } + 75$$

Evaluate

$$\frac{1256-28\sqrt{385}}{9}\approx 78.511147514$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{3}{3}.

$$\left(\frac{1+\sqrt{385}}{3}-\frac{5\times 3}{3}\right)^{2}+75$$

Since \frac{1+\sqrt{385}}{3} and \frac{5\times 3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{1+\sqrt{385}-5\times 3}{3}\right)^{2}+75$$

Do the multiplications in 1+\sqrt{385}-5\times 3.

$$\left(\frac{1+\sqrt{385}-15}{3}\right)^{2}+75$$

Do the calculations in 1+\sqrt{385}-15.

$$\left(\frac{-14+\sqrt{385}}{3}\right)^{2}+75$$

To raise \frac{-14+\sqrt{385}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-14+\sqrt{385}\right)^{2}}{3^{2}}+75$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 75 times \frac{3^{2}}{3^{2}}.

$$\frac{\left(-14+\sqrt{385}\right)^{2}}{3^{2}}+\frac{75\times 3^{2}}{3^{2}}$$

Since \frac{\left(-14+\sqrt{385}\right)^{2}}{3^{2}} and \frac{75\times 3^{2}}{3^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(-14+\sqrt{385}\right)^{2}+75\times 3^{2}}{3^{2}}$$

Do the multiplications in \left(-14+\sqrt{385}\right)^{2}+75\times 3^{2}.

$$\frac{196-28\sqrt{385}+\left(\sqrt{385}\right)^{2}+675}{3^{2}}$$

Do the calculations in 196-28\sqrt{385}+\left(\sqrt{385}\right)^{2}+675.

$$\frac{1256-28\sqrt{385}}{3^{2}}$$

Expand 3^{2}.

$$\frac{1256-28\sqrt{385}}{9}$$

Expand

$$\frac{1256 - 28 \sqrt{385}}{9} = 78.51114751447108$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{3}{3}.

$$\left(\frac{1+\sqrt{385}}{3}-\frac{5\times 3}{3}\right)^{2}+75$$

Since \frac{1+\sqrt{385}}{3} and \frac{5\times 3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{1+\sqrt{385}-5\times 3}{3}\right)^{2}+75$$

Do the multiplications in 1+\sqrt{385}-5\times 3.

$$\left(\frac{1+\sqrt{385}-15}{3}\right)^{2}+75$$

Do the calculations in 1+\sqrt{385}-15.

$$\left(\frac{-14+\sqrt{385}}{3}\right)^{2}+75$$

To raise \frac{-14+\sqrt{385}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-14+\sqrt{385}\right)^{2}}{3^{2}}+75$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 75 times \frac{3^{2}}{3^{2}}.

$$\frac{\left(-14+\sqrt{385}\right)^{2}}{3^{2}}+\frac{75\times 3^{2}}{3^{2}}$$

Since \frac{\left(-14+\sqrt{385}\right)^{2}}{3^{2}} and \frac{75\times 3^{2}}{3^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(-14+\sqrt{385}\right)^{2}+75\times 3^{2}}{3^{2}}$$

Do the multiplications in \left(-14+\sqrt{385}\right)^{2}+75\times 3^{2}.

$$\frac{196-28\sqrt{385}+\left(\sqrt{385}\right)^{2}+675}{3^{2}}$$

Do the calculations in 196-28\sqrt{385}+\left(\sqrt{385}\right)^{2}+675.

$$\frac{1256-28\sqrt{385}}{3^{2}}$$

Expand 3^{2}.

$$\frac{1256-28\sqrt{385}}{9}$$