Solve s^2=19^2-14^2

$$s ^ { 2 } = 19 ^ { 2 } - 14 ^ { 2 }$$

Solve for s

$$s=\sqrt{165}\approx 12.845232579$$

$$s=-\sqrt{165}\approx -12.845232579$$

Steps by Finding Square Root

Calculate 19 to the power of 2 and get 361.

$$s^{2}=361-14^{2}$$

Calculate 14 to the power of 2 and get 196.

$$s^{2}=361-196$$

Subtract 196 from 361 to get 165.

$$s^{2}=165$$

Take the square root of both sides of the equation.

$$s=\sqrt{165} s=-\sqrt{165}$$

Steps Using the Quadratic Formula

Calculate 19 to the power of 2 and get 361.

$$s^{2}=361-14^{2}$$

Calculate 14 to the power of 2 and get 196.

$$s^{2}=361-196$$

Subtract 196 from 361 to get 165.

$$s^{2}=165$$

Subtract 165 from both sides.

$$s^{2}-165=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -165 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$s=\frac{0±\sqrt{0^{2}-4\left(-165\right)}}{2}$$

Square 0.

$$s=\frac{0±\sqrt{-4\left(-165\right)}}{2}$$

Multiply -4 times -165.

$$s=\frac{0±\sqrt{660}}{2}$$

Take the square root of 660.

$$s=\frac{0±2\sqrt{165}}{2}$$

Now solve the equation s=\frac{0±2\sqrt{165}}{2} when ± is plus.

$$s=\sqrt{165}$$

Now solve the equation s=\frac{0±2\sqrt{165}}{2} when ± is minus.

$$s=-\sqrt{165}$$

The equation is now solved.

$$s=\sqrt{165} s=-\sqrt{165}$$