Solve 242-2=L^2

$$242 - 2 = L ^ { 2 }$$

Solve for L

$$L=4\sqrt{15}\approx 15.491933385$$

$$L=-4\sqrt{15}\approx -15.491933385$$

Steps by Finding Square Root

Subtract 2 from 242 to get 240.

$$240=L^{2}$$

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

$$L^{2}=240$$

Take the square root of both sides of the equation.

$$L=4\sqrt{15} L=-4\sqrt{15}$$

Steps Using the Quadratic Formula

Subtract 2 from 242 to get 240.

$$240=L^{2}$$

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

$$L^{2}=240$$

Subtract 240 from both sides.

$$L^{2}-240=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -240 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$L=\frac{0±\sqrt{0^{2}-4\left(-240\right)}}{2}$$

Square 0.

$$L=\frac{0±\sqrt{-4\left(-240\right)}}{2}$$

Multiply -4 times -240.

$$L=\frac{0±\sqrt{960}}{2}$$

Take the square root of 960.

$$L=\frac{0±8\sqrt{15}}{2}$$

Now solve the equation L=\frac{0±8\sqrt{15}}{2} when ± is plus.

$$L=4\sqrt{15}$$

Now solve the equation L=\frac{0±8\sqrt{15}}{2} when ± is minus.

$$L=-4\sqrt{15}$$

The equation is now solved.

$$L=4\sqrt{15} L=-4\sqrt{15}$$