Whakaoti i te 20000=10000*1.015^8+x*1.015^3

$$20000 = 10000 \cdot 1.015 ^ { 8 } + x \cdot 1.015 ^ { 3 }$$

Whakaoti mō x

$$x = \frac{2236178978316014239}{267693664000000} = 8353\frac{133802924014336}{267693664000000} \approx 8353.499835977$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te 1.015 mā te pū o 8, kia riro ko 1.126492586595306937890625.

$$20000=10000\times 1.126492586595306937890625+x\times 1.015^{3}$$

Whakareatia te 10000 ki te 1.126492586595306937890625, ka 11264.92586595306937890625.

$$20000=11264.92586595306937890625+x\times 1.015^{3}$$

Tātaihia te 1.015 mā te pū o 3, kia riro ko 1.045678375.

$$20000=11264.92586595306937890625+x\times 1.045678375$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$11264.92586595306937890625+x\times 1.045678375=20000$$

Tangohia te 11264.92586595306937890625 mai i ngā taha e rua.

$$x\times 1.045678375=20000-11264.92586595306937890625$$

Tangohia te 11264.92586595306937890625 i te 20000, ka 8735.07413404693062109375.

$$x\times 1.045678375=8735.07413404693062109375$$

Whakawehea ngā taha e rua ki te 1.045678375.

$$x=\frac{8735.07413404693062109375}{1.045678375}$$

Whakarohaina te \frac{8735.07413404693062109375}{1.045678375} mā te whakarea i te taurunga me te tauraro ki te 100000000000000000000.

$$x=\frac{873507413404693062109375}{104567837500000000000}$$

Whakahekea te hautanga \frac{873507413404693062109375}{104567837500000000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 390625.

$$x=\frac{2236178978316014239}{267693664000000}$$