Solve 1/2sqrt{(6-2)^2+(9-5)^2}=x

$$\frac { 1 } { 2 } \sqrt { ( 6 - 2 ) ^ { 2 } + ( 9 - 5 ) ^ { 2 } } = x$$

Solve for x

$$x=2\sqrt{2}\approx 2.828427125$$

Steps for Solving Linear Equation

Subtract 2 from 6 to get 4.

$$\frac{1}{2}\sqrt{4^{2}+\left(9-5\right)^{2}}=x$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1}{2}\sqrt{16+\left(9-5\right)^{2}}=x$$

Subtract 5 from 9 to get 4.

$$\frac{1}{2}\sqrt{16+4^{2}}=x$$

Calculate 4 to the power of 2 and get 16.

$$\frac{1}{2}\sqrt{16+16}=x$$

Add 16 and 16 to get 32.

$$\frac{1}{2}\sqrt{32}=x$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{1}{2}\times 4\sqrt{2}=x$$

Multiply \frac{1}{2} and 4 to get 2.

$$2\sqrt{2}=x$$

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

$$x=2\sqrt{2}$$