Solve kL=sqrt{(-2-2)^2+(-2-2)^2+(0-0)^2}

$$k L = \sqrt { ( - 2 - 2 ) ^ { 2 } + ( - 2 - 2 ) ^ { 2 } + ( 0 - 0 ) ^ { 2 } }$$

Solve for L

$$L=\frac{4\sqrt{2}}{k}$$

$$k\neq 0$$

Steps for Solving Linear Equation

Subtract 2 from -2 to get -4.

$$kL=\sqrt{\left(-4\right)^{2}+\left(-2-2\right)^{2}+\left(0-0\right)^{2}}$$

Calculate -4 to the power of 2 and get 16.

$$kL=\sqrt{16+\left(-2-2\right)^{2}+\left(0-0\right)^{2}}$$

Subtract 2 from -2 to get -4.

$$kL=\sqrt{16+\left(-4\right)^{2}+\left(0-0\right)^{2}}$$

Calculate -4 to the power of 2 and get 16.

$$kL=\sqrt{16+16+\left(0-0\right)^{2}}$$

Add 16 and 16 to get 32.

$$kL=\sqrt{32+\left(0-0\right)^{2}}$$

Subtracting 0 from itself leaves 0.

$$kL=\sqrt{32+0^{2}}$$

Calculate 0 to the power of 2 and get 0.

$$kL=\sqrt{32+0}$$

Add 32 and 0 to get 32.

$$kL=\sqrt{32}$$

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}.

$$kL=4\sqrt{2}$$

Divide both sides by k.

$$\frac{kL}{k}=\frac{4\sqrt{2}}{k}$$

Dividing by k undoes the multiplication by k.

$$L=\frac{4\sqrt{2}}{k}$$

Solve for k

$$k=\frac{4\sqrt{2}}{L}$$

$$L\neq 0$$

Steps for Solving Linear Equation

Subtract 2 from -2 to get -4.

$$kL=\sqrt{\left(-4\right)^{2}+\left(-2-2\right)^{2}+\left(0-0\right)^{2}}$$

Calculate -4 to the power of 2 and get 16.

$$kL=\sqrt{16+\left(-2-2\right)^{2}+\left(0-0\right)^{2}}$$

Subtract 2 from -2 to get -4.

$$kL=\sqrt{16+\left(-4\right)^{2}+\left(0-0\right)^{2}}$$

Calculate -4 to the power of 2 and get 16.

$$kL=\sqrt{16+16+\left(0-0\right)^{2}}$$

Add 16 and 16 to get 32.

$$kL=\sqrt{32+\left(0-0\right)^{2}}$$

Subtracting 0 from itself leaves 0.

$$kL=\sqrt{32+0^{2}}$$

Calculate 0 to the power of 2 and get 0.

$$kL=\sqrt{32+0}$$

Add 32 and 0 to get 32.

$$kL=\sqrt{32}$$

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}.

$$kL=4\sqrt{2}$$

The equation is in standard form.

$$Lk=4\sqrt{2}$$

Divide both sides by L.

$$\frac{Lk}{L}=\frac{4\sqrt{2}}{L}$$

Dividing by L undoes the multiplication by L.

$$k=\frac{4\sqrt{2}}{L}$$