Whakaoti i te n^2+7n+5=0

$$n ^ { 2 } + 7 n + 5 = 0$$

Whakaoti mō n

$$n=\frac{\sqrt{29}-7}{2}\approx -0.807417596$$

$$n=\frac{-\sqrt{29}-7}{2}\approx -6.192582404$$

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.

$$n^{2}+7n+5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 7 mō b, me 5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{-7±\sqrt{7^{2}-4\times 5}}{2}$$

Pūrua 7.

$$n=\frac{-7±\sqrt{49-4\times 5}}{2}$$

Whakareatia -4 ki te 5.

$$n=\frac{-7±\sqrt{49-20}}{2}$$

Tāpiri 49 ki te -20.

$$n=\frac{-7±\sqrt{29}}{2}$$

Nā, me whakaoti te whārite n=\frac{-7±\sqrt{29}}{2} ina he tāpiri te ±. Tāpiri -7 ki te \sqrt{29}.

$$n=\frac{\sqrt{29}-7}{2}$$

Nā, me whakaoti te whārite n=\frac{-7±\sqrt{29}}{2} ina he tango te ±. Tango \sqrt{29} mai i -7.

$$n=\frac{-\sqrt{29}-7}{2}$$

Kua oti te whārite te whakatau.

$$n=\frac{\sqrt{29}-7}{2} n=\frac{-\sqrt{29}-7}{2}$$

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.

$$n^{2}+7n+5=0$$

Me tango 5 mai i ngā taha e rua o te whārite.

$$n^{2}+7n+5-5=-5$$

Mā te tango i te 5 i a ia ake anō ka toe ko te 0.

$$n^{2}+7n=-5$$

Whakawehea te 7, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{2}. Nā, tāpiria te pūrua o te \frac{7}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$n^{2}+7n+\left(\frac{7}{2}\right)^{2}=-5+\left(\frac{7}{2}\right)^{2}$$

Pūruatia \frac{7}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$n^{2}+7n+\frac{49}{4}=-5+\frac{49}{4}$$

Tāpiri -5 ki te \frac{49}{4}.

$$n^{2}+7n+\frac{49}{4}=\frac{29}{4}$$

Tauwehea n^{2}+7n+\frac{49}{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}.

$$\left(n+\frac{7}{2}\right)^{2}=\frac{29}{4}$$

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

$$\sqrt{\left(n+\frac{7}{2}\right)^{2}}=\sqrt{\frac{29}{4}}$$

Whakarūnātia.

$$n+\frac{7}{2}=\frac{\sqrt{29}}{2} n+\frac{7}{2}=-\frac{\sqrt{29}}{2}$$

Me tango \frac{7}{2} mai i ngā taha e rua o te whārite.

$$n=\frac{\sqrt{29}-7}{2} n=\frac{-\sqrt{29}-7}{2}$$