Whakaoti i te x^2-3.79x-18.8=3.03

$$x ^ { 2 } - 3.79 x - 18.8 = 3.03$$

Whakaoti mō x

$$x = \frac{\sqrt{1016841} + 379}{200} \approx 6.936926715$$

$$x=\frac{379-\sqrt{1016841}}{200}\approx -3.146926715$$

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.

$$x^{2}-3.79x-18.8=3.03$$

Me tango 3.03 mai i ngā taha e rua o te whārite.

$$x^{2}-3.79x-18.8-3.03=3.03-3.03$$

Mā te tango i te 3.03 i a ia ake anō ka toe ko te 0.

$$x^{2}-3.79x-18.8-3.03=0$$

Tango 3.03 mai i -18.8 mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-3.79x-21.83=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -3.79 mō b, me -21.83 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3.79\right)±\sqrt{\left(-3.79\right)^{2}-4\left(-21.83\right)}}{2}$$

Pūruatia -3.79 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-3.79\right)±\sqrt{14.3641-4\left(-21.83\right)}}{2}$$

Whakareatia -4 ki te -21.83.

$$x=\frac{-\left(-3.79\right)±\sqrt{14.3641+87.32}}{2}$$

Tāpiri 14.3641 ki te 87.32 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.

$$x=\frac{-\left(-3.79\right)±\sqrt{101.6841}}{2}$$

Tuhia te pūtakerua o te 101.6841.

$$x=\frac{-\left(-3.79\right)±\frac{\sqrt{1016841}}{100}}{2}$$

Ko te tauaro o -3.79 ko 3.79.

$$x=\frac{3.79±\frac{\sqrt{1016841}}{100}}{2}$$

Nā, me whakaoti te whārite x=\frac{3.79±\frac{\sqrt{1016841}}{100}}{2} ina he tāpiri te ±. Tāpiri 3.79 ki te \frac{\sqrt{1016841}}{100}.

$$x=\frac{\sqrt{1016841}+379}{2\times 100}$$

Whakawehe \frac{379+\sqrt{1016841}}{100} ki te 2.

$$x=\frac{\sqrt{1016841}+379}{200}$$

Nā, me whakaoti te whārite x=\frac{3.79±\frac{\sqrt{1016841}}{100}}{2} ina he tango te ±. Tango \frac{\sqrt{1016841}}{100} mai i 3.79.

$$x=\frac{379-\sqrt{1016841}}{2\times 100}$$

Whakawehe \frac{379-\sqrt{1016841}}{100} ki te 2.

$$x=\frac{379-\sqrt{1016841}}{200}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{1016841}+379}{200} x=\frac{379-\sqrt{1016841}}{200}$$

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.

$$x^{2}-3.79x-18.8=3.03$$

Me tāpiri 18.8 ki ngā taha e rua o te whārite.

$$x^{2}-3.79x-18.8-\left(-18.8\right)=3.03-\left(-18.8\right)$$

Mā te tango i te -18.8 i a ia ake anō ka toe ko te 0.

$$x^{2}-3.79x=3.03-\left(-18.8\right)$$

Tango -18.8 mai i 3.03 mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-3.79x=21.83$$

Whakawehea te -3.79, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1.895. Nā, tāpiria te pūrua o te -1.895 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-3.79x+\left(-1.895\right)^{2}=21.83+\left(-1.895\right)^{2}$$

Pūruatia -1.895 mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3.79x+3.591025=21.83+3.591025$$

Tāpiri 21.83 ki te 3.591025 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.

$$x^{2}-3.79x+3.591025=25.421025$$

Tauwehea te x^{2}-3.79x+3.591025. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-1.895\right)^{2}=25.421025$$

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

$$\sqrt{\left(x-1.895\right)^{2}}=\sqrt{25.421025}$$

Whakarūnātia.

$$x-1.895=\frac{\sqrt{1016841}}{200} x-1.895=-\frac{\sqrt{1016841}}{200}$$

Me tāpiri 1.895 ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{1016841}+379}{200} x=\frac{379-\sqrt{1016841}}{200}$$