Whakaoti i te 35=2(x-5)^2

$$35 = 2 ( x - 5 ) ^ { 2 }$$

Whakaoti mō x

$$x=\frac{\sqrt{70}}{2}+5\approx 9.183300133$$

$$x=-\frac{\sqrt{70}}{2}+5\approx 0.816699867$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea ngā taha e rua ki te 2.

$$\frac{35}{2}=\left(x-5\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-5\right)^{2}.

$$\frac{35}{2}=x^{2}-10x+25$$

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

$$x^{2}-10x+25=\frac{35}{2}$$

Tangohia te \frac{35}{2} mai i ngā taha e rua.

$$x^{2}-10x+25-\frac{35}{2}=0$$

Tangohia te \frac{35}{2} i te 25, ka \frac{15}{2}.

$$x^{2}-10x+\frac{15}{2}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -10 mō b, me \frac{15}{2} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times \frac{15}{2}}}{2}$$

Pūrua -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times \frac{15}{2}}}{2}$$

Whakareatia -4 ki te \frac{15}{2}.

$$x=\frac{-\left(-10\right)±\sqrt{100-30}}{2}$$

Tāpiri 100 ki te -30.

$$x=\frac{-\left(-10\right)±\sqrt{70}}{2}$$

Ko te tauaro o -10 ko 10.

$$x=\frac{10±\sqrt{70}}{2}$$

Nā, me whakaoti te whārite x=\frac{10±\sqrt{70}}{2} ina he tāpiri te ±. Tāpiri 10 ki te \sqrt{70}.

$$x=\frac{\sqrt{70}+10}{2}$$

Whakawehe 10+\sqrt{70} ki te 2.

$$x=\frac{\sqrt{70}}{2}+5$$

Nā, me whakaoti te whārite x=\frac{10±\sqrt{70}}{2} ina he tango te ±. Tango \sqrt{70} mai i 10.

$$x=\frac{10-\sqrt{70}}{2}$$

Whakawehe 10-\sqrt{70} ki te 2.

$$x=-\frac{\sqrt{70}}{2}+5$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{70}}{2}+5 x=-\frac{\sqrt{70}}{2}+5$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakawehea ngā taha e rua ki te 2.

$$\frac{35}{2}=\left(x-5\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(x-5\right)^{2}.

$$\frac{35}{2}=x^{2}-10x+25$$

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

$$x^{2}-10x+25=\frac{35}{2}$$

Tauwehea te x^{2}-10x+25. 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}.

$$\left(x-5\right)^{2}=\frac{35}{2}$$

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

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{\frac{35}{2}}$$

Whakarūnātia.

$$x-5=\frac{\sqrt{70}}{2} x-5=-\frac{\sqrt{70}}{2}$$

Me tāpiri 5 ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{70}}{2}+5 x=-\frac{\sqrt{70}}{2}+5$$