Whakaoti i te 3n^2+6n-13=-5

$$3 n ^ { 2 } + 6 n - 13 = - 5$$

Whakaoti mō n

$$n=\frac{\sqrt{33}}{3}-1\approx 0.914854216$$

$$n=-\frac{\sqrt{33}}{3}-1\approx -2.914854216$$

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.

$$3n^{2}+6n-13=-5$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$3n^{2}+6n-13-\left(-5\right)=-5-\left(-5\right)$$

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

$$3n^{2}+6n-13-\left(-5\right)=0$$

Tango -5 mai i -13.

$$3n^{2}+6n-8=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 6 mō b, me -8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{-6±\sqrt{6^{2}-4\times 3\left(-8\right)}}{2\times 3}$$

Pūrua 6.

$$n=\frac{-6±\sqrt{36-4\times 3\left(-8\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$n=\frac{-6±\sqrt{36-12\left(-8\right)}}{2\times 3}$$

Whakareatia -12 ki te -8.

$$n=\frac{-6±\sqrt{36+96}}{2\times 3}$$

Tāpiri 36 ki te 96.

$$n=\frac{-6±\sqrt{132}}{2\times 3}$$

Tuhia te pūtakerua o te 132.

$$n=\frac{-6±2\sqrt{33}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$n=\frac{-6±2\sqrt{33}}{6}$$

Nā, me whakaoti te whārite n=\frac{-6±2\sqrt{33}}{6} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{33}.

$$n=\frac{2\sqrt{33}-6}{6}$$

Whakawehe -6+2\sqrt{33} ki te 6.

$$n=\frac{\sqrt{33}}{3}-1$$

Nā, me whakaoti te whārite n=\frac{-6±2\sqrt{33}}{6} ina he tango te ±. Tango 2\sqrt{33} mai i -6.

$$n=\frac{-2\sqrt{33}-6}{6}$$

Whakawehe -6-2\sqrt{33} ki te 6.

$$n=-\frac{\sqrt{33}}{3}-1$$

Kua oti te whārite te whakatau.

$$n=\frac{\sqrt{33}}{3}-1 n=-\frac{\sqrt{33}}{3}-1$$

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.

$$3n^{2}+6n-13=-5$$

Me tāpiri 13 ki ngā taha e rua o te whārite.

$$3n^{2}+6n-13-\left(-13\right)=-5-\left(-13\right)$$

Mā te tango i te -13 i a ia ake anō ka toe ko te 0.

$$3n^{2}+6n=-5-\left(-13\right)$$

Tango -13 mai i -5.

$$3n^{2}+6n=8$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3n^{2}+6n}{3}=\frac{8}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$n^{2}+\frac{6}{3}n=\frac{8}{3}$$

Whakawehe 6 ki te 3.

$$n^{2}+2n=\frac{8}{3}$$

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

$$n^{2}+2n+1^{2}=\frac{8}{3}+1^{2}$$

Pūrua 1.

$$n^{2}+2n+1=\frac{8}{3}+1$$

Tāpiri \frac{8}{3} ki te 1.

$$n^{2}+2n+1=\frac{11}{3}$$

Tauwehea n^{2}+2n+1. 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}.

$$\left(n+1\right)^{2}=\frac{11}{3}$$

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

$$\sqrt{\left(n+1\right)^{2}}=\sqrt{\frac{11}{3}}$$

Whakarūnātia.

$$n+1=\frac{\sqrt{33}}{3} n+1=-\frac{\sqrt{33}}{3}$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$n=\frac{\sqrt{33}}{3}-1 n=-\frac{\sqrt{33}}{3}-1$$