Whakaoti i te 6(135)={left(x-2*1/2right)}^2

$$6(135)= { \left(x-2 \times \frac{ 1 }{ 2 } \right) }^{ 2 }$$

Whakaoti mō x

$$x=9\sqrt{10}+1\approx 29.460498942$$

$$x=1-9\sqrt{10}\approx -27.460498942$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 6 ki te 135, ka 810.

$$810=\left(x-2\times \frac{1}{2}\right)^{2}$$

Whakareatia te 2 ki te \frac{1}{2}, ka 1.

$$810=\left(x-1\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

$$810=x^{2}-2x+1$$

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

$$x^{2}-2x+1=810$$

Tangohia te 810 mai i ngā taha e rua.

$$x^{2}-2x+1-810=0$$

Tangohia te 810 i te 1, ka -809.

$$x^{2}-2x-809=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -809 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-809\right)}}{2}$$

Pūrua -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-809\right)}}{2}$$

Whakareatia -4 ki te -809.

$$x=\frac{-\left(-2\right)±\sqrt{4+3236}}{2}$$

Tāpiri 4 ki te 3236.

$$x=\frac{-\left(-2\right)±\sqrt{3240}}{2}$$

Tuhia te pūtakerua o te 3240.

$$x=\frac{-\left(-2\right)±18\sqrt{10}}{2}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±18\sqrt{10}}{2}$$

Nā, me whakaoti te whārite x=\frac{2±18\sqrt{10}}{2} ina he tāpiri te ±. Tāpiri 2 ki te 18\sqrt{10}.

$$x=\frac{18\sqrt{10}+2}{2}$$

Whakawehe 2+18\sqrt{10} ki te 2.

$$x=9\sqrt{10}+1$$

Nā, me whakaoti te whārite x=\frac{2±18\sqrt{10}}{2} ina he tango te ±. Tango 18\sqrt{10} mai i 2.

$$x=\frac{2-18\sqrt{10}}{2}$$

Whakawehe 2-18\sqrt{10} ki te 2.

$$x=1-9\sqrt{10}$$

Kua oti te whārite te whakatau.

$$x=9\sqrt{10}+1 x=1-9\sqrt{10}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 6 ki te 135, ka 810.

$$810=\left(x-2\times \frac{1}{2}\right)^{2}$$

Whakareatia te 2 ki te \frac{1}{2}, ka 1.

$$810=\left(x-1\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-1\right)^{2}.

$$810=x^{2}-2x+1$$

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

$$x^{2}-2x+1=810$$

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

$$\left(x-1\right)^{2}=810$$

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{810}$$

Whakarūnātia.

$$x-1=9\sqrt{10} x-1=-9\sqrt{10}$$

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

$$x=9\sqrt{10}+1 x=1-9\sqrt{10}$$