Solve K^2=36(16-16*12)^2/20*16*20*16=

$$K ^ { 2 } = \frac { 36 ( 16 - 16 \times 12 ) ^ { 2 } } { 20 \times 16 \times 20 \times 16 } =$$

Solve for K

$$K = \frac{33}{10} = 3\frac{3}{10} = 3.3$$

$$K = -\frac{33}{10} = -3\frac{3}{10} = -3.3$$

Steps Using Difference of Squares

Cancel out 4 in both numerator and denominator.

$$K^{2}=\frac{9\left(16-12\times 16\right)^{2}}{5\times 16\times 16\times 20}$$

Multiply 12 and 16 to get 192.

$$K^{2}=\frac{9\left(16-192\right)^{2}}{5\times 16\times 16\times 20}$$

Subtract 192 from 16 to get -176.

$$K^{2}=\frac{9\left(-176\right)^{2}}{5\times 16\times 16\times 20}$$

Calculate -176 to the power of 2 and get 30976.

$$K^{2}=\frac{9\times 30976}{5\times 16\times 16\times 20}$$

Multiply 9 and 30976 to get 278784.

$$K^{2}=\frac{278784}{5\times 16\times 16\times 20}$$

Multiply 5 and 16 to get 80.

$$K^{2}=\frac{278784}{80\times 16\times 20}$$

Multiply 80 and 16 to get 1280.

$$K^{2}=\frac{278784}{1280\times 20}$$

Multiply 1280 and 20 to get 25600.

$$K^{2}=\frac{278784}{25600}$$

Reduce the fraction \frac{278784}{25600} to lowest terms by extracting and canceling out 256.

$$K^{2}=\frac{1089}{100}$$

Subtract \frac{1089}{100} from both sides.

$$K^{2}-\frac{1089}{100}=0$$

Multiply both sides by 100.

$$100K^{2}-1089=0$$

Consider 100K^{2}-1089. Rewrite 100K^{2}-1089 as \left(10K\right)^{2}-33^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(10K-33\right)\left(10K+33\right)=0$$

To find equation solutions, solve 10K-33=0 and 10K+33=0.

$$K=\frac{33}{10} K=-\frac{33}{10}$$

Steps by Finding Square Root

Cancel out 4 in both numerator and denominator.

$$K^{2}=\frac{9\left(16-12\times 16\right)^{2}}{5\times 16\times 16\times 20}$$

Multiply 12 and 16 to get 192.

$$K^{2}=\frac{9\left(16-192\right)^{2}}{5\times 16\times 16\times 20}$$

Subtract 192 from 16 to get -176.

$$K^{2}=\frac{9\left(-176\right)^{2}}{5\times 16\times 16\times 20}$$

Calculate -176 to the power of 2 and get 30976.

$$K^{2}=\frac{9\times 30976}{5\times 16\times 16\times 20}$$

Multiply 9 and 30976 to get 278784.

$$K^{2}=\frac{278784}{5\times 16\times 16\times 20}$$

Multiply 5 and 16 to get 80.

$$K^{2}=\frac{278784}{80\times 16\times 20}$$

Multiply 80 and 16 to get 1280.

$$K^{2}=\frac{278784}{1280\times 20}$$

Multiply 1280 and 20 to get 25600.

$$K^{2}=\frac{278784}{25600}$$

Reduce the fraction \frac{278784}{25600} to lowest terms by extracting and canceling out 256.

$$K^{2}=\frac{1089}{100}$$

Take the square root of both sides of the equation.

$$K=\frac{33}{10} K=-\frac{33}{10}$$

Steps Using the Quadratic Formula

Cancel out 4 in both numerator and denominator.

$$K^{2}=\frac{9\left(16-12\times 16\right)^{2}}{5\times 16\times 16\times 20}$$

Multiply 12 and 16 to get 192.

$$K^{2}=\frac{9\left(16-192\right)^{2}}{5\times 16\times 16\times 20}$$

Subtract 192 from 16 to get -176.

$$K^{2}=\frac{9\left(-176\right)^{2}}{5\times 16\times 16\times 20}$$

Calculate -176 to the power of 2 and get 30976.

$$K^{2}=\frac{9\times 30976}{5\times 16\times 16\times 20}$$

Multiply 9 and 30976 to get 278784.

$$K^{2}=\frac{278784}{5\times 16\times 16\times 20}$$

Multiply 5 and 16 to get 80.

$$K^{2}=\frac{278784}{80\times 16\times 20}$$

Multiply 80 and 16 to get 1280.

$$K^{2}=\frac{278784}{1280\times 20}$$

Multiply 1280 and 20 to get 25600.

$$K^{2}=\frac{278784}{25600}$$

Reduce the fraction \frac{278784}{25600} to lowest terms by extracting and canceling out 256.

$$K^{2}=\frac{1089}{100}$$

Subtract \frac{1089}{100} from both sides.

$$K^{2}-\frac{1089}{100}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1089}{100} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$K=\frac{0±\sqrt{0^{2}-4\left(-\frac{1089}{100}\right)}}{2}$$

Square 0.

$$K=\frac{0±\sqrt{-4\left(-\frac{1089}{100}\right)}}{2}$$

Multiply -4 times -\frac{1089}{100}.

$$K=\frac{0±\sqrt{\frac{1089}{25}}}{2}$$

Take the square root of \frac{1089}{25}.

$$K=\frac{0±\frac{33}{5}}{2}$$

Now solve the equation K=\frac{0±\frac{33}{5}}{2} when ± is plus.

$$K=\frac{33}{10}$$

Now solve the equation K=\frac{0±\frac{33}{5}}{2} when ± is minus.

$$K=-\frac{33}{10}$$

The equation is now solved.

$$K=\frac{33}{10} K=-\frac{33}{10}$$