Whakaoti i te 9x^2-2=18x

$$9 x ^ { 2 } - 2 = 18 x$$

Whakaoti mō x

$$x=\frac{\sqrt{11}}{3}+1\approx 2.105541597$$

$$x=-\frac{\sqrt{11}}{3}+1\approx -0.105541597$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 18x mai i ngā taha e rua.

$$9x^{2}-2-18x=0$$

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.

$$9x^{2}-18x-2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, -18 mō b, me -2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 9\left(-2\right)}}{2\times 9}$$

Pūrua -18.

$$x=\frac{-\left(-18\right)±\sqrt{324-4\times 9\left(-2\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-\left(-18\right)±\sqrt{324-36\left(-2\right)}}{2\times 9}$$

Whakareatia -36 ki te -2.

$$x=\frac{-\left(-18\right)±\sqrt{324+72}}{2\times 9}$$

Tāpiri 324 ki te 72.

$$x=\frac{-\left(-18\right)±\sqrt{396}}{2\times 9}$$

Tuhia te pūtakerua o te 396.

$$x=\frac{-\left(-18\right)±6\sqrt{11}}{2\times 9}$$

Ko te tauaro o -18 ko 18.

$$x=\frac{18±6\sqrt{11}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{18±6\sqrt{11}}{18}$$

Nā, me whakaoti te whārite x=\frac{18±6\sqrt{11}}{18} ina he tāpiri te ±. Tāpiri 18 ki te 6\sqrt{11}.

$$x=\frac{6\sqrt{11}+18}{18}$$

Whakawehe 18+6\sqrt{11} ki te 18.

$$x=\frac{\sqrt{11}}{3}+1$$

Nā, me whakaoti te whārite x=\frac{18±6\sqrt{11}}{18} ina he tango te ±. Tango 6\sqrt{11} mai i 18.

$$x=\frac{18-6\sqrt{11}}{18}$$

Whakawehe 18-6\sqrt{11} ki te 18.

$$x=-\frac{\sqrt{11}}{3}+1$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{11}}{3}+1 x=-\frac{\sqrt{11}}{3}+1$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 18x mai i ngā taha e rua.

$$9x^{2}-2-18x=0$$

Me tāpiri te 2 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$9x^{2}-18x=2$$

Whakawehea ngā taha e rua ki te 9.

$$\frac{9x^{2}-18x}{9}=\frac{2}{9}$$

Mā te whakawehe ki te 9 ka wetekia te whakareanga ki te 9.

$$x^{2}+\left(-\frac{18}{9}\right)x=\frac{2}{9}$$

Whakawehe -18 ki te 9.

$$x^{2}-2x=\frac{2}{9}$$

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.

$$x^{2}-2x+1=\frac{2}{9}+1$$

Tāpiri \frac{2}{9} ki te 1.

$$x^{2}-2x+1=\frac{11}{9}$$

Tauwehea te x^{2}-2x+1. 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}.

$$\left(x-1\right)^{2}=\frac{11}{9}$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{\frac{11}{9}}$$

Whakarūnātia.

$$x-1=\frac{\sqrt{11}}{3} x-1=-\frac{\sqrt{11}}{3}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{11}}{3}+1 x=-\frac{\sqrt{11}}{3}+1$$