Whakaoti i te 13320=25n^2+25n

$$13320 = 25 n ^ { 2 } + 25 n$$

Whakaoti mō n

$$n=\frac{\sqrt{53305}}{10}-\frac{1}{2}\approx 22.587875606$$

$$n=-\frac{\sqrt{53305}}{10}-\frac{1}{2}\approx -23.587875606$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$25n^{2}+25n=13320$$

Tangohia te 13320 mai i ngā taha e rua.

$$25n^{2}+25n-13320=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 25 mō a, 25 mō b, me -13320 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{-25±\sqrt{25^{2}-4\times 25\left(-13320\right)}}{2\times 25}$$

Pūrua 25.

$$n=\frac{-25±\sqrt{625-4\times 25\left(-13320\right)}}{2\times 25}$$

Whakareatia -4 ki te 25.

$$n=\frac{-25±\sqrt{625-100\left(-13320\right)}}{2\times 25}$$

Whakareatia -100 ki te -13320.

$$n=\frac{-25±\sqrt{625+1332000}}{2\times 25}$$

Tāpiri 625 ki te 1332000.

$$n=\frac{-25±\sqrt{1332625}}{2\times 25}$$

Tuhia te pūtakerua o te 1332625.

$$n=\frac{-25±5\sqrt{53305}}{2\times 25}$$

Whakareatia 2 ki te 25.

$$n=\frac{-25±5\sqrt{53305}}{50}$$

Nā, me whakaoti te whārite n=\frac{-25±5\sqrt{53305}}{50} ina he tāpiri te ±. Tāpiri -25 ki te 5\sqrt{53305}.

$$n=\frac{5\sqrt{53305}-25}{50}$$

Whakawehe -25+5\sqrt{53305} ki te 50.

$$n=\frac{\sqrt{53305}}{10}-\frac{1}{2}$$

Nā, me whakaoti te whārite n=\frac{-25±5\sqrt{53305}}{50} ina he tango te ±. Tango 5\sqrt{53305} mai i -25.

$$n=\frac{-5\sqrt{53305}-25}{50}$$

Whakawehe -25-5\sqrt{53305} ki te 50.

$$n=-\frac{\sqrt{53305}}{10}-\frac{1}{2}$$

Kua oti te whārite te whakatau.

$$n=\frac{\sqrt{53305}}{10}-\frac{1}{2} n=-\frac{\sqrt{53305}}{10}-\frac{1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$25n^{2}+25n=13320$$

Whakawehea ngā taha e rua ki te 25.

$$\frac{25n^{2}+25n}{25}=\frac{13320}{25}$$

Mā te whakawehe ki te 25 ka wetekia te whakareanga ki te 25.

$$n^{2}+\frac{25}{25}n=\frac{13320}{25}$$

Whakawehe 25 ki te 25.

$$n^{2}+n=\frac{13320}{25}$$

Whakahekea te hautanga \frac{13320}{25} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$n^{2}+n=\frac{2664}{5}$$

Whakawehea te 1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{2}. Nā, tāpiria te pūrua o te \frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$n^{2}+n+\left(\frac{1}{2}\right)^{2}=\frac{2664}{5}+\left(\frac{1}{2}\right)^{2}$$

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$n^{2}+n+\frac{1}{4}=\frac{2664}{5}+\frac{1}{4}$$

Tāpiri \frac{2664}{5} ki te \frac{1}{4} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$n^{2}+n+\frac{1}{4}=\frac{10661}{20}$$

Tauwehea n^{2}+n+\frac{1}{4}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(n+\frac{1}{2}\right)^{2}=\frac{10661}{20}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(n+\frac{1}{2}\right)^{2}}=\sqrt{\frac{10661}{20}}$$

Whakarūnātia.

$$n+\frac{1}{2}=\frac{\sqrt{53305}}{10} n+\frac{1}{2}=-\frac{\sqrt{53305}}{10}$$

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$n=\frac{\sqrt{53305}}{10}-\frac{1}{2} n=-\frac{\sqrt{53305}}{10}-\frac{1}{2}$$