Solve frac{(6,78*10^{6}m)^{2}-2*(2,28*10^11m)^2}{-2(2,28*10^11m)^2}

$$\frac { ( 6,78 \cdot 10 ^ { 6 } m ) ^ { 2 } - 2 \cdot ( 2,28 \cdot 10 ^ { 11 } m ) ^ { 2 } } { - 2 ( 2,28 \cdot 10 ^ { 11 } m ) ^ { 2 } }$$

Evaluate

$$\frac{28879999987231}{28880000000000}\approx 1$$

Solution Steps

Calculate 10 to the power of 6 and get 1000000.

$$\frac{\left(6,78\times 1000000m\right)^{2}-2\times \left(2,28\times 10^{11}m\right)^{2}}{-2\times \left(2,28\times 10^{11}m\right)^{2}}$$

Multiply 6,78 and 1000000 to get 6780000.

$$\frac{\left(6780000m\right)^{2}-2\times \left(2,28\times 10^{11}m\right)^{2}}{-2\times \left(2,28\times 10^{11}m\right)^{2}}$$

Expand \left(6780000m\right)^{2}.

$$\frac{6780000^{2}m^{2}-2\times \left(2,28\times 10^{11}m\right)^{2}}{-2\times \left(2,28\times 10^{11}m\right)^{2}}$$

Calculate 6780000 to the power of 2 and get 45968400000000.

$$\frac{45968400000000m^{2}-2\times \left(2,28\times 10^{11}m\right)^{2}}{-2\times \left(2,28\times 10^{11}m\right)^{2}}$$

Calculate 10 to the power of 11 and get 100000000000.

$$\frac{45968400000000m^{2}-2\times \left(2,28\times 100000000000m\right)^{2}}{-2\times \left(2,28\times 10^{11}m\right)^{2}}$$

Multiply 2,28 and 100000000000 to get 228000000000.

$$\frac{45968400000000m^{2}-2\times \left(228000000000m\right)^{2}}{-2\times \left(2,28\times 10^{11}m\right)^{2}}$$

Expand \left(228000000000m\right)^{2}.

$$\frac{45968400000000m^{2}-2\times 228000000000^{2}m^{2}}{-2\times \left(2,28\times 10^{11}m\right)^{2}}$$

Calculate 228000000000 to the power of 2 and get 51984000000000000000000.

$$\frac{45968400000000m^{2}-2\times 51984000000000000000000m^{2}}{-2\times \left(2,28\times 10^{11}m\right)^{2}}$$

Multiply 2 and 51984000000000000000000 to get 103968000000000000000000.

$$\frac{45968400000000m^{2}-103968000000000000000000m^{2}}{-2\times \left(2,28\times 10^{11}m\right)^{2}}$$

Combine 45968400000000m^{2} and -103968000000000000000000m^{2} to get -103967999954031600000000m^{2}.

$$\frac{-103967999954031600000000m^{2}}{-2\times \left(2,28\times 10^{11}m\right)^{2}}$$

Calculate 10 to the power of 11 and get 100000000000.

$$\frac{-103967999954031600000000m^{2}}{-2\times \left(2,28\times 100000000000m\right)^{2}}$$

Multiply 2,28 and 100000000000 to get 228000000000.

$$\frac{-103967999954031600000000m^{2}}{-2\times \left(228000000000m\right)^{2}}$$

Expand \left(228000000000m\right)^{2}.

$$\frac{-103967999954031600000000m^{2}}{-2\times 228000000000^{2}m^{2}}$$

Calculate 228000000000 to the power of 2 and get 51984000000000000000000.

$$\frac{-103967999954031600000000m^{2}}{-2\times 51984000000000000000000m^{2}}$$

Multiply -2 and 51984000000000000000000 to get -103968000000000000000000.

$$\frac{-103967999954031600000000m^{2}}{-103968000000000000000000m^{2}}$$

Cancel out 3600000000m^{2} in both numerator and denominator.

$$\frac{-28879999987231}{-28880000000000}$$

Fraction \frac{-28879999987231}{-28880000000000} can be simplified to \frac{28879999987231}{28880000000000} by removing the negative sign from both the numerator and the denominator.

$$\frac{28879999987231}{28880000000000}$$

Factor

$$\frac{41 \cdot 89 \cdot 7914497119}{2 ^ {13} \cdot 5 ^ {10} \cdot 19 ^ {2}} = 0.9999999995578601$$