Whakaoti i te 0=(x-5)^2-6

$$0 = ( x - 5 ) ^ { 2 } - 6$$

Whakaoti mō x

$$x=\sqrt{6}+5\approx 7.449489743$$

$$x=5-\sqrt{6}\approx 2.550510257$$

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-5\right)^{2}.

$$0=x^{2}-10x+25-6$$

Tangohia te 6 i te 25, ka 19.

$$0=x^{2}-10x+19$$

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

$$x^{2}-10x+19=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -10 mō b, me 19 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 19}}{2}$$

Pūrua -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times 19}}{2}$$

Whakareatia -4 ki te 19.

$$x=\frac{-\left(-10\right)±\sqrt{100-76}}{2}$$

Tāpiri 100 ki te -76.

$$x=\frac{-\left(-10\right)±\sqrt{24}}{2}$$

Tuhia te pūtakerua o te 24.

$$x=\frac{-\left(-10\right)±2\sqrt{6}}{2}$$

Ko te tauaro o -10 ko 10.

$$x=\frac{10±2\sqrt{6}}{2}$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{6}}{2} ina he tāpiri te ±. Tāpiri 10 ki te 2\sqrt{6}.

$$x=\frac{2\sqrt{6}+10}{2}$$

Whakawehe 10+2\sqrt{6} ki te 2.

$$x=\sqrt{6}+5$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{6}}{2} ina he tango te ±. Tango 2\sqrt{6} mai i 10.

$$x=\frac{10-2\sqrt{6}}{2}$$

Whakawehe 10-2\sqrt{6} ki te 2.

$$x=5-\sqrt{6}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{6}+5 x=5-\sqrt{6}$$

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-5\right)^{2}.

$$0=x^{2}-10x+25-6$$

Tangohia te 6 i te 25, ka 19.

$$0=x^{2}-10x+19$$

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

$$x^{2}-10x+19=0$$

Tangohia te 19 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}-10x=-19$$

Whakawehea te -10, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -5. Nā, tāpiria te pūrua o te -5 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-10x+\left(-5\right)^{2}=-19+\left(-5\right)^{2}$$

Pūrua -5.

$$x^{2}-10x+25=-19+25$$

Tāpiri -19 ki te 25.

$$x^{2}-10x+25=6$$

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

$$\left(x-5\right)^{2}=6$$

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

$$\sqrt{\left(x-5\right)^{2}}=\sqrt{6}$$

Whakarūnātia.

$$x-5=\sqrt{6} x-5=-\sqrt{6}$$

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

$$x=\sqrt{6}+5 x=5-\sqrt{6}$$