Solve -16{left(5/4right)}^2+405/4+4

$$-16 { \left( \frac{ 5 }{ 4 } \right) }^{ 2 } +40 \frac{ 5 }{ 4 } +4$$

Evaluate

$$\frac{81}{4}=20.25$$

Solution Steps

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$-16\times \frac{25}{16}+\frac{40\times 4+5}{4}+4$$

Multiply -16 times \frac{25}{16}.

$$-25+\frac{40\times 4+5}{4}+4$$

Multiply 40 and 4 to get 160.

$$-25+\frac{160+5}{4}+4$$

Add 160 and 5 to get 165.

$$-25+\frac{165}{4}+4$$

Convert -25 to fraction -\frac{100}{4}.

$$-\frac{100}{4}+\frac{165}{4}+4$$

Since -\frac{100}{4} and \frac{165}{4} have the same denominator, add them by adding their numerators.

$$\frac{-100+165}{4}+4$$

Add -100 and 165 to get 65.

$$\frac{65}{4}+4$$

Convert 4 to fraction \frac{16}{4}.

$$\frac{65}{4}+\frac{16}{4}$$

Since \frac{65}{4} and \frac{16}{4} have the same denominator, add them by adding their numerators.

$$\frac{65+16}{4}$$

Add 65 and 16 to get 81.

$$\frac{81}{4}$$

Factor

$$\frac{3 ^ {4}}{2 ^ {2}} = 20\frac{1}{4} = 20.25$$