Whakaoti i te 0=x^2-8x-2

$$0 = { x }^{ 2 } -8x-2$$

Whakaoti mō x

$$x=3\sqrt{2}+4\approx 8.242640687$$

$$x=4-3\sqrt{2}\approx -0.242640687$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}-8x-2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -8 mō b, me -2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-2\right)}}{2}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-2\right)}}{2}$$

Whakareatia -4 ki te -2.

$$x=\frac{-\left(-8\right)±\sqrt{64+8}}{2}$$

Tāpiri 64 ki te 8.

$$x=\frac{-\left(-8\right)±\sqrt{72}}{2}$$

Tuhia te pūtakerua o te 72.

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

Ko te tauaro o -8 ko 8.

$$x=\frac{8±6\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{8±6\sqrt{2}}{2} ina he tāpiri te ±. Tāpiri 8 ki te 6\sqrt{2}.

$$x=\frac{6\sqrt{2}+8}{2}$$

Whakawehe 8+6\sqrt{2} ki te 2.

$$x=3\sqrt{2}+4$$

Nā, me whakaoti te whārite x=\frac{8±6\sqrt{2}}{2} ina he tango te ±. Tango 6\sqrt{2} mai i 8.

$$x=\frac{8-6\sqrt{2}}{2}$$

Whakawehe 8-6\sqrt{2} ki te 2.

$$x=4-3\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=3\sqrt{2}+4 x=4-3\sqrt{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}-8x-2=0$$

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

$$x^{2}-8x=2$$

Whakawehea te -8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -4. Nā, tāpiria te pūrua o te -4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-8x+\left(-4\right)^{2}=2+\left(-4\right)^{2}$$

Pūrua -4.

$$x^{2}-8x+16=2+16$$

Tāpiri 2 ki te 16.

$$x^{2}-8x+16=18$$

Tauwehea x^{2}-8x+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}.

$$\left(x-4\right)^{2}=18$$

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

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

Whakarūnātia.

$$x-4=3\sqrt{2} x-4=-3\sqrt{2}$$

Me tāpiri 4 ki ngā taha e rua o te whārite.

$$x=3\sqrt{2}+4 x=4-3\sqrt{2}$$