Solve (3/2-5/8+3/4)^2+(3/2-frac{7}{2})^2

$$( \frac { 3 } { 2 } - \frac { 5 } { 8 } + \frac { 3 } { 4 } ) ^ { 2 } + ( \frac { 3 } { 2 } - \frac { 7 } { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{425}{64}=6.640625$$

Solution Steps

Subtract \frac{5}{8} from \frac{3}{2} to get \frac{7}{8}.

$$\left(\frac{7}{8}+\frac{3}{4}\right)^{2}+\left(\frac{3}{2}-\frac{7}{2}\right)^{2}$$

Add \frac{7}{8} and \frac{3}{4} to get \frac{13}{8}.

$$\left(\frac{13}{8}\right)^{2}+\left(\frac{3}{2}-\frac{7}{2}\right)^{2}$$

Calculate \frac{13}{8} to the power of 2 and get \frac{169}{64}.

$$\frac{169}{64}+\left(\frac{3}{2}-\frac{7}{2}\right)^{2}$$

Subtract \frac{7}{2} from \frac{3}{2} to get -2.

$$\frac{169}{64}+\left(-2\right)^{2}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{169}{64}+4$$

Add \frac{169}{64} and 4 to get \frac{425}{64}.

$$\frac{425}{64}$$

Factor

$$\frac{5 ^ {2} \cdot 17}{2 ^ {6}} = 6\frac{41}{64} = 6.640625$$