Whakaoti i te x^2-23x-2.100=0

$$x ^ { 2 } - 23 x - 2.100 = 0$$

Whakaoti mō x

$$x=\frac{\sqrt{13435}}{10}+11.5\approx 23.090944741$$

$$x=-\frac{\sqrt{13435}}{10}+11.5\approx -0.090944741$$

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.

$$x^{2}-23x-2.1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -23 mō b, me -2.1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-23\right)±\sqrt{\left(-23\right)^{2}-4\left(-2.1\right)}}{2}$$

Pūrua -23.

$$x=\frac{-\left(-23\right)±\sqrt{529-4\left(-2.1\right)}}{2}$$

Whakareatia -4 ki te -2.1.

$$x=\frac{-\left(-23\right)±\sqrt{529+8.4}}{2}$$

Tāpiri 529 ki te 8.4.

$$x=\frac{-\left(-23\right)±\sqrt{537.4}}{2}$$

Tuhia te pūtakerua o te 537.4.

$$x=\frac{-\left(-23\right)±\frac{\sqrt{13435}}{5}}{2}$$

Ko te tauaro o -23 ko 23.

$$x=\frac{23±\frac{\sqrt{13435}}{5}}{2}$$

Nā, me whakaoti te whārite x=\frac{23±\frac{\sqrt{13435}}{5}}{2} ina he tāpiri te ±. Tāpiri 23 ki te \frac{\sqrt{13435}}{5}.

$$x=\frac{\frac{\sqrt{13435}}{5}+23}{2}$$

Whakawehe 23+\frac{\sqrt{13435}}{5} ki te 2.

$$x=\frac{\sqrt{13435}}{10}+\frac{23}{2}$$

Nā, me whakaoti te whārite x=\frac{23±\frac{\sqrt{13435}}{5}}{2} ina he tango te ±. Tango \frac{\sqrt{13435}}{5} mai i 23.

$$x=\frac{-\frac{\sqrt{13435}}{5}+23}{2}$$

Whakawehe 23-\frac{\sqrt{13435}}{5} ki te 2.

$$x=-\frac{\sqrt{13435}}{10}+\frac{23}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{13435}}{10}+\frac{23}{2} x=-\frac{\sqrt{13435}}{10}+\frac{23}{2}$$

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.

$$x^{2}-23x-2.1=0$$

Me tāpiri 2.1 ki ngā taha e rua o te whārite.

$$x^{2}-23x-2.1-\left(-2.1\right)=-\left(-2.1\right)$$

Mā te tango i te -2.1 i a ia ake anō ka toe ko te 0.

$$x^{2}-23x=-\left(-2.1\right)$$

Tango -2.1 mai i 0.

$$x^{2}-23x=2.1$$

Whakawehea te -23, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{23}{2}. Nā, tāpiria te pūrua o te -\frac{23}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-23x+\left(-\frac{23}{2}\right)^{2}=2.1+\left(-\frac{23}{2}\right)^{2}$$

Pūruatia -\frac{23}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-23x+\frac{529}{4}=2.1+\frac{529}{4}$$

Tāpiri 2.1 ki te \frac{529}{4} 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.

$$x^{2}-23x+\frac{529}{4}=\frac{2687}{20}$$

Tauwehea x^{2}-23x+\frac{529}{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}.

$$\left(x-\frac{23}{2}\right)^{2}=\frac{2687}{20}$$

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

$$\sqrt{\left(x-\frac{23}{2}\right)^{2}}=\sqrt{\frac{2687}{20}}$$

Whakarūnātia.

$$x-\frac{23}{2}=\frac{\sqrt{13435}}{10} x-\frac{23}{2}=-\frac{\sqrt{13435}}{10}$$

Me tāpiri \frac{23}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{13435}}{10}+\frac{23}{2} x=-\frac{\sqrt{13435}}{10}+\frac{23}{2}$$