Whakaoti i te 2x^2-5x-6=0

$$2 x ^ { 2 } - 5 x - 6 = 0$$

Whakaoti mō x

$$x = \frac{\sqrt{73} + 5}{4} \approx 3.386000936$$

$$x=\frac{5-\sqrt{73}}{4}\approx -0.886000936$$

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.

$$2x^{2}-5x-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -5 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 2\left(-6\right)}}{2\times 2}$$

Pūrua -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 2\left(-6\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-5\right)±\sqrt{25-8\left(-6\right)}}{2\times 2}$$

Whakareatia -8 ki te -6.

$$x=\frac{-\left(-5\right)±\sqrt{25+48}}{2\times 2}$$

Tāpiri 25 ki te 48.

$$x=\frac{-\left(-5\right)±\sqrt{73}}{2\times 2}$$

Ko te tauaro o -5 ko 5.

$$x=\frac{5±\sqrt{73}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{5±\sqrt{73}}{4}$$

Nā, me whakaoti te whārite x=\frac{5±\sqrt{73}}{4} ina he tāpiri te ±. Tāpiri 5 ki te \sqrt{73}.

$$x=\frac{\sqrt{73}+5}{4}$$

Nā, me whakaoti te whārite x=\frac{5±\sqrt{73}}{4} ina he tango te ±. Tango \sqrt{73} mai i 5.

$$x=\frac{5-\sqrt{73}}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{73}+5}{4} x=\frac{5-\sqrt{73}}{4}$$

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.

$$2x^{2}-5x-6=0$$

Me tāpiri 6 ki ngā taha e rua o te whārite.

$$2x^{2}-5x-6-\left(-6\right)=-\left(-6\right)$$

Mā te tango i te -6 i a ia ake anō ka toe ko te 0.

$$2x^{2}-5x=-\left(-6\right)$$

Tango -6 mai i 0.

$$2x^{2}-5x=6$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-5x}{2}=\frac{6}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}-\frac{5}{2}x=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$x^{2}-\frac{5}{2}x=3$$

Whakawehea te -\frac{5}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{4}. Nā, tāpiria te pūrua o te -\frac{5}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{5}{2}x+\left(-\frac{5}{4}\right)^{2}=3+\left(-\frac{5}{4}\right)^{2}$$

Pūruatia -\frac{5}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{5}{2}x+\frac{25}{16}=3+\frac{25}{16}$$

Tāpiri 3 ki te \frac{25}{16}.

$$x^{2}-\frac{5}{2}x+\frac{25}{16}=\frac{73}{16}$$

Tauwehea x^{2}-\frac{5}{2}x+\frac{25}{16}. 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}.

$$\left(x-\frac{5}{4}\right)^{2}=\frac{73}{16}$$

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

$$\sqrt{\left(x-\frac{5}{4}\right)^{2}}=\sqrt{\frac{73}{16}}$$

Whakarūnātia.

$$x-\frac{5}{4}=\frac{\sqrt{73}}{4} x-\frac{5}{4}=-\frac{\sqrt{73}}{4}$$

Me tāpiri \frac{5}{4} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{73}+5}{4} x=\frac{5-\sqrt{73}}{4}$$