Solve 12^2-6^2=b^2

$$12 ^ { 2 } - 6 ^ { 2 } = b ^ { 2 }$$

Solve for b

$$b=6\sqrt{3}\approx 10.392304845$$

$$b=-6\sqrt{3}\approx -10.392304845$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$144-6^{2}=b^{2}$$

Calculate 6 to the power of 2 and get 36.

$$144-36=b^{2}$$

Subtract 36 from 144 to get 108.

$$108=b^{2}$$

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

$$b^{2}=108$$

Take the square root of both sides of the equation.

$$b=6\sqrt{3} b=-6\sqrt{3}$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$144-6^{2}=b^{2}$$

Calculate 6 to the power of 2 and get 36.

$$144-36=b^{2}$$

Subtract 36 from 144 to get 108.

$$108=b^{2}$$

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

$$b^{2}=108$$

Subtract 108 from both sides.

$$b^{2}-108=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -108 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-108\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-108\right)}}{2}$$

Multiply -4 times -108.

$$b=\frac{0±\sqrt{432}}{2}$$

Take the square root of 432.

$$b=\frac{0±12\sqrt{3}}{2}$$

Now solve the equation b=\frac{0±12\sqrt{3}}{2} when ± is plus.

$$b=6\sqrt{3}$$

Now solve the equation b=\frac{0±12\sqrt{3}}{2} when ± is minus.

$$b=-6\sqrt{3}$$

The equation is now solved.

$$b=6\sqrt{3} b=-6\sqrt{3}$$