Consider $\left(7-\sqrt{5}\right)\left(7+\sqrt{5}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
Consider $\left(7+\sqrt{5}\right)\left(7-\sqrt{5}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
Do the calculations in $54+14\sqrt{5}-54+14\sqrt{5}$.
$$\frac{28\sqrt{5}}{44}=a+7\sqrt{56}$$
Factor $56=2^{2}\times 14$. Rewrite the square root of the product $\sqrt{2^{2}\times 14}$ as the product of square roots $\sqrt{2^{2}}\sqrt{14}$. Take the square root of $2^{2}$.
$$\frac{28\sqrt{5}}{44}=a+7\times 2\sqrt{14}$$
Multiply $7$ and $2$ to get $14$.
$$\frac{28\sqrt{5}}{44}=a+14\sqrt{14}$$
Divide $28\sqrt{5}$ by $44$ to get $\frac{7}{11}\sqrt{5}$.
$$\frac{7}{11}\sqrt{5}=a+14\sqrt{14}$$
Swap sides so that all variable terms are on the left hand side.
