Solve AC=sqrt{6-(-2)^2+(-3-1)^2}

$$A C = \sqrt { 6 - ( - 2 ) ^ { 2 } + ( - 3 - 1 ) ^ { 2 } }$$

Solve for A

$$A=\frac{3\sqrt{2}}{C}$$

$$C\neq 0$$

Steps for Solving Linear Equation

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

$$AC=\sqrt{6-4+\left(-3-1\right)^{2}}$$

Subtract 4 from 6 to get 2.

$$AC=\sqrt{2+\left(-3-1\right)^{2}}$$

Subtract 1 from -3 to get -4.

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

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

$$AC=\sqrt{2+16}$$

Add 2 and 16 to get 18.

$$AC=\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$AC=3\sqrt{2}$$

The equation is in standard form.

$$CA=3\sqrt{2}$$

Divide both sides by C.

$$\frac{CA}{C}=\frac{3\sqrt{2}}{C}$$

Dividing by C undoes the multiplication by C.

$$A=\frac{3\sqrt{2}}{C}$$

Solve for C

$$C=\frac{3\sqrt{2}}{A}$$

$$A\neq 0$$

Steps for Solving Linear Equation

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

$$AC=\sqrt{6-4+\left(-3-1\right)^{2}}$$

Subtract 4 from 6 to get 2.

$$AC=\sqrt{2+\left(-3-1\right)^{2}}$$

Subtract 1 from -3 to get -4.

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

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

$$AC=\sqrt{2+16}$$

Add 2 and 16 to get 18.

$$AC=\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$AC=3\sqrt{2}$$

Divide both sides by A.

$$\frac{AC}{A}=\frac{3\sqrt{2}}{A}$$

Dividing by A undoes the multiplication by A.

$$C=\frac{3\sqrt{2}}{A}$$