Solve K^2=400*(6*300-20*74)^2/26*374*80*320=

$$K ^ { 2 } = \frac { 400 \times ( 6 \times 300 - 20 \times 74 ) ^ { 2 } } { 26 \times 374 \times 80 \times 320 } =$$

Solve for K

$$K=\frac{20\sqrt{2431}}{2431}\approx 0.405636957$$

$$K=-\frac{20\sqrt{2431}}{2431}\approx -0.405636957$$

Steps by Finding Square Root

Cancel out 2\times 2\times 5\times 20 in both numerator and denominator.

$$K^{2}=\frac{\left(6\times 300-20\times 74\right)^{2}}{4\times 13\times 64\times 187}$$

Multiply 6 and 300 to get 1800.

$$K^{2}=\frac{\left(1800-20\times 74\right)^{2}}{4\times 13\times 64\times 187}$$

Multiply 20 and 74 to get 1480.

$$K^{2}=\frac{\left(1800-1480\right)^{2}}{4\times 13\times 64\times 187}$$

Subtract 1480 from 1800 to get 320.

$$K^{2}=\frac{320^{2}}{4\times 13\times 64\times 187}$$

Calculate 320 to the power of 2 and get 102400.

$$K^{2}=\frac{102400}{4\times 13\times 64\times 187}$$

Multiply 4 and 13 to get 52.

$$K^{2}=\frac{102400}{52\times 64\times 187}$$

Multiply 52 and 64 to get 3328.

$$K^{2}=\frac{102400}{3328\times 187}$$

Multiply 3328 and 187 to get 622336.

$$K^{2}=\frac{102400}{622336}$$

Reduce the fraction \frac{102400}{622336} to lowest terms by extracting and canceling out 256.

$$K^{2}=\frac{400}{2431}$$

Take the square root of both sides of the equation.

$$K=\frac{20\sqrt{2431}}{2431} K=-\frac{20\sqrt{2431}}{2431}$$

Steps Using the Quadratic Formula

Cancel out 2\times 2\times 5\times 20 in both numerator and denominator.

$$K^{2}=\frac{\left(6\times 300-20\times 74\right)^{2}}{4\times 13\times 64\times 187}$$

Multiply 6 and 300 to get 1800.

$$K^{2}=\frac{\left(1800-20\times 74\right)^{2}}{4\times 13\times 64\times 187}$$

Multiply 20 and 74 to get 1480.

$$K^{2}=\frac{\left(1800-1480\right)^{2}}{4\times 13\times 64\times 187}$$

Subtract 1480 from 1800 to get 320.

$$K^{2}=\frac{320^{2}}{4\times 13\times 64\times 187}$$

Calculate 320 to the power of 2 and get 102400.

$$K^{2}=\frac{102400}{4\times 13\times 64\times 187}$$

Multiply 4 and 13 to get 52.

$$K^{2}=\frac{102400}{52\times 64\times 187}$$

Multiply 52 and 64 to get 3328.

$$K^{2}=\frac{102400}{3328\times 187}$$

Multiply 3328 and 187 to get 622336.

$$K^{2}=\frac{102400}{622336}$$

Reduce the fraction \frac{102400}{622336} to lowest terms by extracting and canceling out 256.

$$K^{2}=\frac{400}{2431}$$

Subtract \frac{400}{2431} from both sides.

$$K^{2}-\frac{400}{2431}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{400}{2431} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$K=\frac{0±\sqrt{0^{2}-4\left(-\frac{400}{2431}\right)}}{2}$$

Square 0.

$$K=\frac{0±\sqrt{-4\left(-\frac{400}{2431}\right)}}{2}$$

Multiply -4 times -\frac{400}{2431}.

$$K=\frac{0±\sqrt{\frac{1600}{2431}}}{2}$$

Take the square root of \frac{1600}{2431}.

$$K=\frac{0±\frac{40\sqrt{2431}}{2431}}{2}$$

Now solve the equation K=\frac{0±\frac{40\sqrt{2431}}{2431}}{2} when ± is plus.

$$K=\frac{20\sqrt{2431}}{2431}$$

Now solve the equation K=\frac{0±\frac{40\sqrt{2431}}{2431}}{2} when ± is minus.

$$K=-\frac{20\sqrt{2431}}{2431}$$

The equation is now solved.

$$K=\frac{20\sqrt{2431}}{2431} K=-\frac{20\sqrt{2431}}{2431}$$