Solve 5/15=28^2+14^2-b^2/200*14*28

$$\frac { 5 } { 15 } = \frac { 28 ^ { 2 } + 14 ^ { 2 } - b ^ { 2 } } { 200 \times 14 \times 28 }$$

Solve for b

$$b=-\frac{14\sqrt{1155}i}{3}\approx -0-158.598024368i$$

$$b=\frac{14\sqrt{1155}i}{3}\approx 158.598024368i$$

Steps by Finding Square Root

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{1}{3}=\frac{28^{2}+14^{2}-b^{2}}{200\times 14\times 28}$$

Calculate 28 to the power of 2 and get 784.

$$\frac{1}{3}=\frac{784+14^{2}-b^{2}}{200\times 14\times 28}$$

Calculate 14 to the power of 2 and get 196.

$$\frac{1}{3}=\frac{784+196-b^{2}}{200\times 14\times 28}$$

Add 784 and 196 to get 980.

$$\frac{1}{3}=\frac{980-b^{2}}{200\times 14\times 28}$$

Multiply 200 and 14 to get 2800.

$$\frac{1}{3}=\frac{980-b^{2}}{2800\times 28}$$

Multiply 2800 and 28 to get 78400.

$$\frac{1}{3}=\frac{980-b^{2}}{78400}$$

Divide each term of 980-b^{2} by 78400 to get \frac{1}{80}-\frac{1}{78400}b^{2}.

$$\frac{1}{3}=\frac{1}{80}-\frac{1}{78400}b^{2}$$

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

$$\frac{1}{80}-\frac{1}{78400}b^{2}=\frac{1}{3}$$

Subtract \frac{1}{80} from both sides.

$$-\frac{1}{78400}b^{2}=\frac{1}{3}-\frac{1}{80}$$

Subtract \frac{1}{80} from \frac{1}{3} to get \frac{77}{240}.

$$-\frac{1}{78400}b^{2}=\frac{77}{240}$$

Multiply both sides by -78400, the reciprocal of -\frac{1}{78400}.

$$b^{2}=\frac{77}{240}\left(-78400\right)$$

Multiply \frac{77}{240} and -78400 to get -\frac{75460}{3}.

$$b^{2}=-\frac{75460}{3}$$

The equation is now solved.

$$b=\frac{14\sqrt{1155}i}{3} b=-\frac{14\sqrt{1155}i}{3}$$

Steps Using the Quadratic Formula

Reduce the fraction \frac{5}{15} to lowest terms by extracting and canceling out 5.

$$\frac{1}{3}=\frac{28^{2}+14^{2}-b^{2}}{200\times 14\times 28}$$

Calculate 28 to the power of 2 and get 784.

$$\frac{1}{3}=\frac{784+14^{2}-b^{2}}{200\times 14\times 28}$$

Calculate 14 to the power of 2 and get 196.

$$\frac{1}{3}=\frac{784+196-b^{2}}{200\times 14\times 28}$$

Add 784 and 196 to get 980.

$$\frac{1}{3}=\frac{980-b^{2}}{200\times 14\times 28}$$

Multiply 200 and 14 to get 2800.

$$\frac{1}{3}=\frac{980-b^{2}}{2800\times 28}$$

Multiply 2800 and 28 to get 78400.

$$\frac{1}{3}=\frac{980-b^{2}}{78400}$$

Divide each term of 980-b^{2} by 78400 to get \frac{1}{80}-\frac{1}{78400}b^{2}.

$$\frac{1}{3}=\frac{1}{80}-\frac{1}{78400}b^{2}$$

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

$$\frac{1}{80}-\frac{1}{78400}b^{2}=\frac{1}{3}$$

Subtract \frac{1}{3} from both sides.

$$\frac{1}{80}-\frac{1}{78400}b^{2}-\frac{1}{3}=0$$

Subtract \frac{1}{3} from \frac{1}{80} to get -\frac{77}{240}.

$$-\frac{77}{240}-\frac{1}{78400}b^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-\frac{1}{78400}b^{2}-\frac{77}{240}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{78400} for a, 0 for b, and -\frac{77}{240} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{78400}\right)\left(-\frac{77}{240}\right)}}{2\left(-\frac{1}{78400}\right)}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-\frac{1}{78400}\right)\left(-\frac{77}{240}\right)}}{2\left(-\frac{1}{78400}\right)}$$

Multiply -4 times -\frac{1}{78400}.

$$b=\frac{0±\sqrt{\frac{1}{19600}\left(-\frac{77}{240}\right)}}{2\left(-\frac{1}{78400}\right)}$$

Multiply \frac{1}{19600} times -\frac{77}{240} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$b=\frac{0±\sqrt{-\frac{11}{672000}}}{2\left(-\frac{1}{78400}\right)}$$

Take the square root of -\frac{11}{672000}.

$$b=\frac{0±\frac{\sqrt{1155}i}{8400}}{2\left(-\frac{1}{78400}\right)}$$

Multiply 2 times -\frac{1}{78400}.

$$b=\frac{0±\frac{\sqrt{1155}i}{8400}}{-\frac{1}{39200}}$$

Now solve the equation b=\frac{0±\frac{\sqrt{1155}i}{8400}}{-\frac{1}{39200}} when ± is plus.

$$b=-\frac{14\sqrt{1155}i}{3}$$

Now solve the equation b=\frac{0±\frac{\sqrt{1155}i}{8400}}{-\frac{1}{39200}} when ± is minus.

$$b=\frac{14\sqrt{1155}i}{3}$$

The equation is now solved.

$$b=-\frac{14\sqrt{1155}i}{3} b=\frac{14\sqrt{1155}i}{3}$$