Solve 81x=12+147+2sqrt{2}sqrt{147}

$$81x = 12+147+2 \sqrt{ 2 } \sqrt{ 147 }$$

Solve for x

$$x=\frac{14\sqrt{6}}{81}+\frac{53}{27}\approx 2.38633156$$

Steps for Solving Linear Equation

Add 12 and 147 to get 159.

$$81x=159+2\sqrt{2}\sqrt{147}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$81x=159+2\sqrt{2}\times 7\sqrt{3}$$

Multiply 2 and 7 to get 14.

$$81x=159+14\sqrt{2}\sqrt{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$81x=159+14\sqrt{6}$$

The equation is in standard form.

$$81x=14\sqrt{6}+159$$

Divide both sides by 81.

$$\frac{81x}{81}=\frac{14\sqrt{6}+159}{81}$$

Dividing by 81 undoes the multiplication by 81.

$$x=\frac{14\sqrt{6}+159}{81}$$

Divide 159+14\sqrt{6} by 81.

$$x=\frac{14\sqrt{6}}{81}+\frac{53}{27}$$