Solve (2.50+2.97/2)^2-(4.35+4.80/2)^2/2*(2.17+3.42+3.87+4.35)

$$\frac { ( \frac { 2.50 + 2.97 } { 2 } ) ^ { 2 } - ( \frac { 4.35 + 4.80 } { 2 } ) ^ { 2 } } { 2 \times ( 2.17 + 3.42 + 3.87 + 4.35 ) }$$

Evaluate

$$-\frac{16813}{34525}\approx -0.486980449$$

Solution Steps

Add 2.5 and 2.97 to get 5.47.

$$\frac{\left(\frac{5.47}{2}\right)^{2}-\left(\frac{4.35+4.8}{2}\right)^{2}}{2\left(2.17+3.42+3.87+4.35\right)}$$

Expand \frac{5.47}{2} by multiplying both numerator and the denominator by 100.

$$\frac{\left(\frac{547}{200}\right)^{2}-\left(\frac{4.35+4.8}{2}\right)^{2}}{2\left(2.17+3.42+3.87+4.35\right)}$$

Calculate \frac{547}{200} to the power of 2 and get \frac{299209}{40000}.

$$\frac{\frac{299209}{40000}-\left(\frac{4.35+4.8}{2}\right)^{2}}{2\left(2.17+3.42+3.87+4.35\right)}$$

Add 4.35 and 4.8 to get 9.15.

$$\frac{\frac{299209}{40000}-\left(\frac{9.15}{2}\right)^{2}}{2\left(2.17+3.42+3.87+4.35\right)}$$

Expand \frac{9.15}{2} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{299209}{40000}-\left(\frac{915}{200}\right)^{2}}{2\left(2.17+3.42+3.87+4.35\right)}$$

Reduce the fraction \frac{915}{200} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{299209}{40000}-\left(\frac{183}{40}\right)^{2}}{2\left(2.17+3.42+3.87+4.35\right)}$$

Calculate \frac{183}{40} to the power of 2 and get \frac{33489}{1600}.

$$\frac{\frac{299209}{40000}-\frac{33489}{1600}}{2\left(2.17+3.42+3.87+4.35\right)}$$

Subtract \frac{33489}{1600} from \frac{299209}{40000} to get -\frac{16813}{1250}.

$$\frac{-\frac{16813}{1250}}{2\left(2.17+3.42+3.87+4.35\right)}$$

Add 2.17 and 3.42 to get 5.59.

$$\frac{-\frac{16813}{1250}}{2\left(5.59+3.87+4.35\right)}$$

Add 5.59 and 3.87 to get 9.46.

$$\frac{-\frac{16813}{1250}}{2\left(9.46+4.35\right)}$$

Add 9.46 and 4.35 to get 13.81.

$$\frac{-\frac{16813}{1250}}{2\times 13.81}$$

Multiply 2 and 13.81 to get 27.62.

$$\frac{-\frac{16813}{1250}}{27.62}$$

Express \frac{-\frac{16813}{1250}}{27.62} as a single fraction.

$$\frac{-16813}{1250\times 27.62}$$

Multiply 1250 and 27.62 to get 34525.

$$\frac{-16813}{34525}$$

Fraction \frac{-16813}{34525} can be rewritten as -\frac{16813}{34525} by extracting the negative sign.

$$-\frac{16813}{34525}$$

Factor

$$-\frac{16813}{34525} = -0.4869804489500362$$