Whakaoti i te (x-2)^2-4x+2=0

$$( x - 2 ) ^ { 2 } - 4 x + 2 = 0$$

Whakaoti mō x

$$x=\sqrt{10}+4\approx 7.16227766$$

$$x=4-\sqrt{10}\approx 0.83772234$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-2\right)^{2}.

$$x^{2}-4x+4-4x+2=0$$

Pahekotia te -4x me -4x, ka -8x.

$$x^{2}-8x+4+2=0$$

Tāpirihia te 4 ki te 2, ka 6.

$$x^{2}-8x+6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -8 mō b, me 6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 6}}{2}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 6}}{2}$$

Whakareatia -4 ki te 6.

$$x=\frac{-\left(-8\right)±\sqrt{64-24}}{2}$$

Tāpiri 64 ki te -24.

$$x=\frac{-\left(-8\right)±\sqrt{40}}{2}$$

Tuhia te pūtakerua o te 40.

$$x=\frac{-\left(-8\right)±2\sqrt{10}}{2}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±2\sqrt{10}}{2}$$

Nā, me whakaoti te whārite x=\frac{8±2\sqrt{10}}{2} ina he tāpiri te ±. Tāpiri 8 ki te 2\sqrt{10}.

$$x=\frac{2\sqrt{10}+8}{2}$$

Whakawehe 8+2\sqrt{10} ki te 2.

$$x=\sqrt{10}+4$$

Nā, me whakaoti te whārite x=\frac{8±2\sqrt{10}}{2} ina he tango te ±. Tango 2\sqrt{10} mai i 8.

$$x=\frac{8-2\sqrt{10}}{2}$$

Whakawehe 8-2\sqrt{10} ki te 2.

$$x=4-\sqrt{10}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{10}+4 x=4-\sqrt{10}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-2\right)^{2}.

$$x^{2}-4x+4-4x+2=0$$

Pahekotia te -4x me -4x, ka -8x.

$$x^{2}-8x+4+2=0$$

Tāpirihia te 4 ki te 2, ka 6.

$$x^{2}-8x+6=0$$

Tangohia te 6 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-8x=-6$$

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.

$$x^{2}-8x+\left(-4\right)^{2}=-6+\left(-4\right)^{2}$$

Pūrua -4.

$$x^{2}-8x+16=-6+16$$

Tāpiri -6 ki te 16.

$$x^{2}-8x+16=10$$

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}.

$$\left(x-4\right)^{2}=10$$

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

$$\sqrt{\left(x-4\right)^{2}}=\sqrt{10}$$

Whakarūnātia.

$$x-4=\sqrt{10} x-4=-\sqrt{10}$$

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

$$x=\sqrt{10}+4 x=4-\sqrt{10}$$