Question

$$-15(9+4\sqrt{5}+1}{9+4\sqrt{5}})-10(\frac{9+4\sqrt{5}+1}{9+4\sqrt{5}})+9$$

Answer

-691-200*sqrt(5)

Solution


Collect like terms.
\[-15((9+19)+(4\sqrt{5}+4\sqrt{5}))-10((9+19)+(4\sqrt{5}+4\sqrt{5}))+9\]
Simplify  \((9+19)+(4\sqrt{5}+4\sqrt{5})\)  to  \(28+8\sqrt{5}\).
\[-15(28+8\sqrt{5})-10(9+19+4\sqrt{5}+4\sqrt{5})+9\]
Collect like terms.
\[-15(28+8\sqrt{5})-10((9+19)+(4\sqrt{5}+4\sqrt{5}))+9\]
Simplify  \((9+19)+(4\sqrt{5}+4\sqrt{5})\)  to  \(28+8\sqrt{5}\).
\[-15(28+8\sqrt{5})-10(28+8\sqrt{5})+9\]
Collect like terms.
\[(-15(28+8\sqrt{5})-10(28+8\sqrt{5}))+9\]
Simplify.
\[-25(28+8\sqrt{5})+9\]
Expand by distributing terms.
\[-(700+200\sqrt{5})+9\]
Remove parentheses.
\[-700-200\sqrt{5}+9\]
Simplify.
\[-691-200\sqrt{5}\]

Decimal Form: -1138.213596