Solve a^2=14^2+6^2

$$a ^ { 2 } = 14 ^ { 2 } + 6 ^ { 2 }$$

Solve for a

$$a=2\sqrt{58}\approx 15.231546212$$

$$a=-2\sqrt{58}\approx -15.231546212$$

Steps by Finding Square Root

Calculate 14 to the power of 2 and get 196.

$$a^{2}=196+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$a^{2}=196+36$$

Add 196 and 36 to get 232.

$$a^{2}=232$$

Take the square root of both sides of the equation.

$$a=2\sqrt{58} a=-2\sqrt{58}$$

Steps Using the Quadratic Formula

Calculate 14 to the power of 2 and get 196.

$$a^{2}=196+6^{2}$$

Calculate 6 to the power of 2 and get 36.

$$a^{2}=196+36$$

Add 196 and 36 to get 232.

$$a^{2}=232$$

Subtract 232 from both sides.

$$a^{2}-232=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -232 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-232\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-232\right)}}{2}$$

Multiply -4 times -232.

$$a=\frac{0±\sqrt{928}}{2}$$

Take the square root of 928.

$$a=\frac{0±4\sqrt{58}}{2}$$

Now solve the equation a=\frac{0±4\sqrt{58}}{2} when ± is plus.

$$a=2\sqrt{58}$$

Now solve the equation a=\frac{0±4\sqrt{58}}{2} when ± is minus.

$$a=-2\sqrt{58}$$

The equation is now solved.

$$a=2\sqrt{58} a=-2\sqrt{58}$$