Solve CO=sqrt{(38^2-1440^2)}

$$C O = \sqrt { ( 38 ^ { 2 } - 1440 ^ { 2 } ) }$$

Solve for C

$$C=\frac{2\sqrt{518039}i}{O}$$

$$O\neq 0$$

Steps for Solving Linear Equation

Calculate 38 to the power of 2 and get 1444.

$$CO=\sqrt{1444-1440^{2}}$$

Calculate 1440 to the power of 2 and get 2073600.

$$CO=\sqrt{1444-2073600}$$

Subtract 2073600 from 1444 to get -2072156.

$$CO=\sqrt{-2072156}$$

Factor -2072156=\left(2i\right)^{2}\times 518039. Rewrite the square root of the product \sqrt{\left(2i\right)^{2}\times 518039} as the product of square roots \sqrt{\left(2i\right)^{2}}\sqrt{518039}. Take the square root of \left(2i\right)^{2}.

$$CO=2i\sqrt{518039}$$

Reorder the terms.

$$CO=2\sqrt{518039}i$$

The equation is in standard form.

$$OC=2\sqrt{518039}i$$

Divide both sides by O.

$$\frac{OC}{O}=\frac{2\sqrt{518039}i}{O}$$

Dividing by O undoes the multiplication by O.

$$C=\frac{2\sqrt{518039}i}{O}$$

Solve for O

$$O=\frac{2\sqrt{518039}i}{C}$$

$$C\neq 0$$

Steps for Solving Linear Equation

Calculate 38 to the power of 2 and get 1444.

$$CO=\sqrt{1444-1440^{2}}$$

Calculate 1440 to the power of 2 and get 2073600.

$$CO=\sqrt{1444-2073600}$$

Subtract 2073600 from 1444 to get -2072156.

$$CO=\sqrt{-2072156}$$

Factor -2072156=\left(2i\right)^{2}\times 518039. Rewrite the square root of the product \sqrt{\left(2i\right)^{2}\times 518039} as the product of square roots \sqrt{\left(2i\right)^{2}}\sqrt{518039}. Take the square root of \left(2i\right)^{2}.

$$CO=2i\sqrt{518039}$$

Reorder the terms.

$$CO=2\sqrt{518039}i$$

Divide both sides by C.

$$\frac{CO}{C}=\frac{2\sqrt{518039}i}{C}$$

Dividing by C undoes the multiplication by C.

$$O=\frac{2\sqrt{518039}i}{C}$$