Solve x=2+sqrt{45}-1/2sqrt{328}

$$x = 2 + \sqrt { 45 } - \frac { 1 } { 2 } \sqrt { 328 }$$

Solve for x

$$x=3\sqrt{5}+2-\sqrt{82}\approx -0.347181206$$

Steps for Solving Linear Equation

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$x=2+3\sqrt{5}-\frac{1}{2}\sqrt{328}$$

Factor 328=2^{2}\times 82. Rewrite the square root of the product \sqrt{2^{2}\times 82} as the product of square roots \sqrt{2^{2}}\sqrt{82}. Take the square root of 2^{2}.

$$x=2+3\sqrt{5}-\frac{1}{2}\times 2\sqrt{82}$$

Cancel out 2 and 2.

$$x=2+3\sqrt{5}-\sqrt{82}$$

Assign x

$$x≔3\sqrt{5}+2-\sqrt{82}$$