Solve A=sqrt{frac{a-sqrt{10+2sqrt{9}}}{5}}

$$A = \sqrt { \frac { a - \sqrt { 10 + 2 \sqrt { 9 } } } { 5 } }$$

Solve for a

$$a=5A^{2}+4$$

$$A\geq 0$$

Steps for Solving Radical Equations

Calculate the square root of 9 and get 3.

$$A=\sqrt{\frac{a-\sqrt{10+2\times 3}}{5}}$$

Multiply 2 and 3 to get 6.

$$A=\sqrt{\frac{a-\sqrt{10+6}}{5}}$$

Add 10 and 6 to get 16.

$$A=\sqrt{\frac{a-\sqrt{16}}{5}}$$

Calculate the square root of 16 and get 4.

$$A=\sqrt{\frac{a-4}{5}}$$

Divide each term of a-4 by 5 to get \frac{1}{5}a-\frac{4}{5}.

$$A=\sqrt{\frac{1}{5}a-\frac{4}{5}}$$

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{\frac{1}{5}a-\frac{4}{5}}=A$$

Square both sides of the equation.

$$\frac{1}{5}a-\frac{4}{5}=A^{2}$$

Add \frac{4}{5} to both sides of the equation.

$$\frac{1}{5}a-\frac{4}{5}-\left(-\frac{4}{5}\right)=A^{2}-\left(-\frac{4}{5}\right)$$

Subtracting -\frac{4}{5} from itself leaves 0.

$$\frac{1}{5}a=A^{2}-\left(-\frac{4}{5}\right)$$

Subtract -\frac{4}{5} from A^{2}.

$$\frac{1}{5}a=A^{2}+\frac{4}{5}$$

Multiply both sides by 5.

$$\frac{\frac{1}{5}a}{\frac{1}{5}}=\frac{A^{2}+\frac{4}{5}}{\frac{1}{5}}$$

Dividing by \frac{1}{5} undoes the multiplication by \frac{1}{5}.

$$a=\frac{A^{2}+\frac{4}{5}}{\frac{1}{5}}$$

Divide A^{2}+\frac{4}{5} by \frac{1}{5} by multiplying A^{2}+\frac{4}{5} by the reciprocal of \frac{1}{5}.

$$a=5A^{2}+4$$

Solve for A (complex solution)

$$A=\frac{\sqrt{5\left(a-4\right)}}{5}$$

Solve for a (complex solution)

$$a=5A^{2}+4$$

$$arg(A)<\pi \text{ or }A=0$$

Solve for A

$$A=\frac{\sqrt{5\left(a-4\right)}}{5}$$

$$a\geq 4$$