Solve CE=sqrt{(-sqrt{6}-3sqrt{2}-2sqrt{6})^2+(sqrt{2}+sqrt{3}+2sqrt{2})}

$$C E = \sqrt { ( - \sqrt { 6 } - 3 \sqrt { 2 } - 2 \sqrt { 6 } ) ^ { 2 } + ( \sqrt { 2 } + \sqrt { 3 } + 2 \sqrt { 2 } ) }$$

Solve for C

$$C=\frac{\sqrt{3\sqrt{2}+37\sqrt{3}+72}}{E}$$

$$E\neq 0$$

Steps for Solving Linear Equation

Square -\sqrt{6}-3\sqrt{2}-2\sqrt{6}.

$$CE=\sqrt{12\sqrt{2}\sqrt{6}-6\left(-\sqrt{6}\right)\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$CE=\sqrt{12\sqrt{2}\sqrt{2}\sqrt{3}-6\left(-\sqrt{6}\right)\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$CE=\sqrt{12\times 2\sqrt{3}-6\left(-\sqrt{6}\right)\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply 12 and 2 to get 24.

$$CE=\sqrt{24\sqrt{3}-6\left(-\sqrt{6}\right)\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply -6 and -1 to get 6.

$$CE=\sqrt{24\sqrt{3}+6\sqrt{6}\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$CE=\sqrt{24\sqrt{3}+6\sqrt{2}\sqrt{3}\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply -4 and -1 to get 4.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\sqrt{6}\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

The square of \sqrt{6} is 6.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+4\times 6+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply 4 and 6 to get 24.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+24+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

The square of \sqrt{2} is 2.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+24+9\times 2+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply 9 and 2 to get 18.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+24+18+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Add 24 and 18 to get 42.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+42+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Calculate -\sqrt{6} to the power of 2 and get \left(\sqrt{6}\right)^{2}.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+42+\left(\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Do the multiplications.

$$CE=\sqrt{24\sqrt{3}+12\sqrt{3}+24+42+\left(\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Combine 24\sqrt{3} and 12\sqrt{3} to get 36\sqrt{3}.

$$CE=\sqrt{36\sqrt{3}+24+42+\left(\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Add 24 and 42 to get 66.

$$CE=\sqrt{36\sqrt{3}+66+\left(\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

The square of \sqrt{6} is 6.

$$CE=\sqrt{36\sqrt{3}+66+6+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Add 66 and 6 to get 72.

$$CE=\sqrt{36\sqrt{3}+72+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Combine 36\sqrt{3} and \sqrt{3} to get 37\sqrt{3}.

$$CE=\sqrt{37\sqrt{3}+72+\sqrt{2}+2\sqrt{2}}$$

Combine \sqrt{2} and 2\sqrt{2} to get 3\sqrt{2}.

$$CE=\sqrt{37\sqrt{3}+72+3\sqrt{2}}$$

The equation is in standard form.

$$EC=\sqrt{3\sqrt{2}+37\sqrt{3}+72}$$

Divide both sides by E.

$$\frac{EC}{E}=\frac{\sqrt{3\sqrt{2}+37\sqrt{3}+72}}{E}$$

Dividing by E undoes the multiplication by E.

$$C=\frac{\sqrt{3\sqrt{2}+37\sqrt{3}+72}}{E}$$

Solve for E

$$E=\frac{\sqrt{3\sqrt{2}+37\sqrt{3}+72}}{C}$$

$$C\neq 0$$

Steps for Solving Linear Equation

Square -\sqrt{6}-3\sqrt{2}-2\sqrt{6}.

$$CE=\sqrt{12\sqrt{2}\sqrt{6}-6\left(-\sqrt{6}\right)\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$CE=\sqrt{12\sqrt{2}\sqrt{2}\sqrt{3}-6\left(-\sqrt{6}\right)\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$CE=\sqrt{12\times 2\sqrt{3}-6\left(-\sqrt{6}\right)\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply 12 and 2 to get 24.

$$CE=\sqrt{24\sqrt{3}-6\left(-\sqrt{6}\right)\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply -6 and -1 to get 6.

$$CE=\sqrt{24\sqrt{3}+6\sqrt{6}\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$CE=\sqrt{24\sqrt{3}+6\sqrt{2}\sqrt{3}\sqrt{2}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}-4\left(-\sqrt{6}\right)\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply -4 and -1 to get 4.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\sqrt{6}\sqrt{6}+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+4\left(\sqrt{6}\right)^{2}+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

The square of \sqrt{6} is 6.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+4\times 6+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply 4 and 6 to get 24.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+24+9\left(\sqrt{2}\right)^{2}+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

The square of \sqrt{2} is 2.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+24+9\times 2+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Multiply 9 and 2 to get 18.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+24+18+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Add 24 and 18 to get 42.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+42+\left(-\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Calculate -\sqrt{6} to the power of 2 and get \left(\sqrt{6}\right)^{2}.

$$CE=\sqrt{24\sqrt{3}+6\times 2\sqrt{3}+4\times 6+42+\left(\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Do the multiplications.

$$CE=\sqrt{24\sqrt{3}+12\sqrt{3}+24+42+\left(\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Combine 24\sqrt{3} and 12\sqrt{3} to get 36\sqrt{3}.

$$CE=\sqrt{36\sqrt{3}+24+42+\left(\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Add 24 and 42 to get 66.

$$CE=\sqrt{36\sqrt{3}+66+\left(\sqrt{6}\right)^{2}+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

The square of \sqrt{6} is 6.

$$CE=\sqrt{36\sqrt{3}+66+6+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Add 66 and 6 to get 72.

$$CE=\sqrt{36\sqrt{3}+72+\sqrt{2}+\sqrt{3}+2\sqrt{2}}$$

Combine 36\sqrt{3} and \sqrt{3} to get 37\sqrt{3}.

$$CE=\sqrt{37\sqrt{3}+72+\sqrt{2}+2\sqrt{2}}$$

Combine \sqrt{2} and 2\sqrt{2} to get 3\sqrt{2}.

$$CE=\sqrt{37\sqrt{3}+72+3\sqrt{2}}$$

The equation is in standard form.

$$CE=\sqrt{3\sqrt{2}+37\sqrt{3}+72}$$

Divide both sides by C.

$$\frac{CE}{C}=\frac{\sqrt{3\sqrt{2}+37\sqrt{3}+72}}{C}$$

Dividing by C undoes the multiplication by C.

$$E=\frac{\sqrt{3\sqrt{2}+37\sqrt{3}+72}}{C}$$