Whakaoti i te n^2+301258n-1205032=0

$$n ^ { 2 } + 301258 n - 1205032 = 0$$

Whakaoti mō n

$$n=\sqrt{22690300673}-150629\approx 3.999946891$$

$$n=-\sqrt{22690300673}-150629\approx -301261.999946891$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$n^{2}+301258n-1205032=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 301258 mō b, me -1205032 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{-301258±\sqrt{301258^{2}-4\left(-1205032\right)}}{2}$$

Pūrua 301258.

$$n=\frac{-301258±\sqrt{90756382564-4\left(-1205032\right)}}{2}$$

Whakareatia -4 ki te -1205032.

$$n=\frac{-301258±\sqrt{90756382564+4820128}}{2}$$

Tāpiri 90756382564 ki te 4820128.

$$n=\frac{-301258±\sqrt{90761202692}}{2}$$

Tuhia te pūtakerua o te 90761202692.

$$n=\frac{-301258±2\sqrt{22690300673}}{2}$$

Nā, me whakaoti te whārite n=\frac{-301258±2\sqrt{22690300673}}{2} ina he tāpiri te ±. Tāpiri -301258 ki te 2\sqrt{22690300673}.

$$n=\frac{2\sqrt{22690300673}-301258}{2}$$

Whakawehe -301258+2\sqrt{22690300673} ki te 2.

$$n=\sqrt{22690300673}-150629$$

Nā, me whakaoti te whārite n=\frac{-301258±2\sqrt{22690300673}}{2} ina he tango te ±. Tango 2\sqrt{22690300673} mai i -301258.

$$n=\frac{-2\sqrt{22690300673}-301258}{2}$$

Whakawehe -301258-2\sqrt{22690300673} ki te 2.

$$n=-\sqrt{22690300673}-150629$$

Kua oti te whārite te whakatau.

$$n=\sqrt{22690300673}-150629 n=-\sqrt{22690300673}-150629$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$n^{2}+301258n-1205032=0$$

Me tāpiri 1205032 ki ngā taha e rua o te whārite.

$$n^{2}+301258n-1205032-\left(-1205032\right)=-\left(-1205032\right)$$

Mā te tango i te -1205032 i a ia ake anō ka toe ko te 0.

$$n^{2}+301258n=-\left(-1205032\right)$$

Tango -1205032 mai i 0.

$$n^{2}+301258n=1205032$$

Whakawehea te 301258, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 150629. Nā, tāpiria te pūrua o te 150629 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$n^{2}+301258n+150629^{2}=1205032+150629^{2}$$

Pūrua 150629.

$$n^{2}+301258n+22689095641=1205032+22689095641$$

Tāpiri 1205032 ki te 22689095641.

$$n^{2}+301258n+22689095641=22690300673$$

Tauwehea n^{2}+301258n+22689095641. 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}.

$$\left(n+150629\right)^{2}=22690300673$$

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

$$\sqrt{\left(n+150629\right)^{2}}=\sqrt{22690300673}$$

Whakarūnātia.

$$n+150629=\sqrt{22690300673} n+150629=-\sqrt{22690300673}$$

Me tango 150629 mai i ngā taha e rua o te whārite.

$$n=\sqrt{22690300673}-150629 n=-\sqrt{22690300673}-150629$$