Whakaoti i te 8+3g^2-9g=188

$$8 + 3 g ^ { 2 } - 9 g = 188$$

Whakaoti mō g

$$g = \frac{\sqrt{249} + 3}{2} \approx 9.389866919$$

$$g=\frac{3-\sqrt{249}}{2}\approx -6.389866919$$

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.

$$3g^{2}-9g+8=188$$

Me tango 188 mai i ngā taha e rua o te whārite.

$$3g^{2}-9g+8-188=188-188$$

Mā te tango i te 188 i a ia ake anō ka toe ko te 0.

$$3g^{2}-9g+8-188=0$$

Tango 188 mai i 8.

$$3g^{2}-9g-180=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -9 mō b, me -180 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$g=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 3\left(-180\right)}}{2\times 3}$$

Pūrua -9.

$$g=\frac{-\left(-9\right)±\sqrt{81-4\times 3\left(-180\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$g=\frac{-\left(-9\right)±\sqrt{81-12\left(-180\right)}}{2\times 3}$$

Whakareatia -12 ki te -180.

$$g=\frac{-\left(-9\right)±\sqrt{81+2160}}{2\times 3}$$

Tāpiri 81 ki te 2160.

$$g=\frac{-\left(-9\right)±\sqrt{2241}}{2\times 3}$$

Tuhia te pūtakerua o te 2241.

$$g=\frac{-\left(-9\right)±3\sqrt{249}}{2\times 3}$$

Ko te tauaro o -9 ko 9.

$$g=\frac{9±3\sqrt{249}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$g=\frac{9±3\sqrt{249}}{6}$$

Nā, me whakaoti te whārite g=\frac{9±3\sqrt{249}}{6} ina he tāpiri te ±. Tāpiri 9 ki te 3\sqrt{249}.

$$g=\frac{3\sqrt{249}+9}{6}$$

Whakawehe 9+3\sqrt{249} ki te 6.

$$g=\frac{\sqrt{249}+3}{2}$$

Nā, me whakaoti te whārite g=\frac{9±3\sqrt{249}}{6} ina he tango te ±. Tango 3\sqrt{249} mai i 9.

$$g=\frac{9-3\sqrt{249}}{6}$$

Whakawehe 9-3\sqrt{249} ki te 6.

$$g=\frac{3-\sqrt{249}}{2}$$

Kua oti te whārite te whakatau.

$$g=\frac{\sqrt{249}+3}{2} g=\frac{3-\sqrt{249}}{2}$$

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.

$$3g^{2}-9g+8=188$$

Me tango 8 mai i ngā taha e rua o te whārite.

$$3g^{2}-9g+8-8=188-8$$

Mā te tango i te 8 i a ia ake anō ka toe ko te 0.

$$3g^{2}-9g=188-8$$

Tango 8 mai i 188.

$$3g^{2}-9g=180$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3g^{2}-9g}{3}=\frac{180}{3}$$

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

$$g^{2}+\left(-\frac{9}{3}\right)g=\frac{180}{3}$$

Whakawehe -9 ki te 3.

$$g^{2}-3g=\frac{180}{3}$$

Whakawehe 180 ki te 3.

$$g^{2}-3g=60$$

Whakawehea te -3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{2}. Nā, tāpiria te pūrua o te -\frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$g^{2}-3g+\left(-\frac{3}{2}\right)^{2}=60+\left(-\frac{3}{2}\right)^{2}$$

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$g^{2}-3g+\frac{9}{4}=60+\frac{9}{4}$$

Tāpiri 60 ki te \frac{9}{4}.

$$g^{2}-3g+\frac{9}{4}=\frac{249}{4}$$

Tauwehea g^{2}-3g+\frac{9}{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}.

$$\left(g-\frac{3}{2}\right)^{2}=\frac{249}{4}$$

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

$$\sqrt{\left(g-\frac{3}{2}\right)^{2}}=\sqrt{\frac{249}{4}}$$

Whakarūnātia.

$$g-\frac{3}{2}=\frac{\sqrt{249}}{2} g-\frac{3}{2}=-\frac{\sqrt{249}}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$g=\frac{\sqrt{249}+3}{2} g=\frac{3-\sqrt{249}}{2}$$