Solve frac{(sqrt{0,09}*1/2*0,7)^2-(0,7-1/3)^2}{3/2-sqrt{0,25}}

$$\frac { ( \sqrt { 0,09 } \cdot \frac { 1 } { 2 } \cdot 0,7 ) ^ { 2 } - ( 0,7 - \frac { 1 } { 3 } ) ^ { 2 } } { \frac { 3 } { 2 } - \sqrt { 0,25 } }$$

Evaluate

$$-\frac{44431}{360000}\approx -0,123419444$$

Solution Steps

Calculate the square root of 0,09 and get 0,3.

$$\frac{\left(0,7\times 0,3\times \frac{1}{2}\right)^{2}-\left(0,7-\frac{1}{3}\right)^{2}}{\frac{3}{2}-\sqrt{0,25}}$$

Multiply 0,7 and 0,3 to get 0,21.

$$\frac{\left(0,21\times \frac{1}{2}\right)^{2}-\left(0,7-\frac{1}{3}\right)^{2}}{\frac{3}{2}-\sqrt{0,25}}$$

Multiply 0,21 and \frac{1}{2} to get \frac{21}{200}.

$$\frac{\left(\frac{21}{200}\right)^{2}-\left(0,7-\frac{1}{3}\right)^{2}}{\frac{3}{2}-\sqrt{0,25}}$$

Calculate \frac{21}{200} to the power of 2 and get \frac{441}{40000}.

$$\frac{\frac{441}{40000}-\left(0,7-\frac{1}{3}\right)^{2}}{\frac{3}{2}-\sqrt{0,25}}$$

Subtract \frac{1}{3} from 0,7 to get \frac{11}{30}.

$$\frac{\frac{441}{40000}-\left(\frac{11}{30}\right)^{2}}{\frac{3}{2}-\sqrt{0,25}}$$

Calculate \frac{11}{30} to the power of 2 and get \frac{121}{900}.

$$\frac{\frac{441}{40000}-\frac{121}{900}}{\frac{3}{2}-\sqrt{0,25}}$$

Subtract \frac{121}{900} from \frac{441}{40000} to get -\frac{44431}{360000}.

$$\frac{-\frac{44431}{360000}}{\frac{3}{2}-\sqrt{0,25}}$$

Calculate the square root of 0,25 and get 0,5.

$$\frac{-\frac{44431}{360000}}{\frac{3}{2}-0,5}$$

Subtract 0,5 from \frac{3}{2} to get 1.

$$\frac{-\frac{44431}{360000}}{1}$$

Anything divided by one gives itself.

$$-\frac{44431}{360000}$$

Factor

$$-\frac{44431}{360000} = -0.12341944444444444$$