Whakaoti i te 0=9left(x+1right)^2-8

$$0=9 { \left(x+1 \right) }^{ 2 } -8$$

Whakaoti mō x

$$x=\frac{2\sqrt{2}}{3}-1\approx -0.057190958$$

$$x=-\frac{2\sqrt{2}}{3}-1\approx -1.942809042$$

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+1\right)^{2}.

$$0=9\left(x^{2}+2x+1\right)-8$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te x^{2}+2x+1.

$$0=9x^{2}+18x+9-8$$

Tangohia te 8 i te 9, ka 1.

$$0=9x^{2}+18x+1$$

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

$$9x^{2}+18x+1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, 18 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\times 9}}{2\times 9}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\times 9}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-18±\sqrt{324-36}}{2\times 9}$$

Tāpiri 324 ki te -36.

$$x=\frac{-18±\sqrt{288}}{2\times 9}$$

Tuhia te pūtakerua o te 288.

$$x=\frac{-18±12\sqrt{2}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{-18±12\sqrt{2}}{18}$$

Nā, me whakaoti te whārite x=\frac{-18±12\sqrt{2}}{18} ina he tāpiri te ±. Tāpiri -18 ki te 12\sqrt{2}.

$$x=\frac{12\sqrt{2}-18}{18}$$

Whakawehe -18+12\sqrt{2} ki te 18.

$$x=\frac{2\sqrt{2}}{3}-1$$

Nā, me whakaoti te whārite x=\frac{-18±12\sqrt{2}}{18} ina he tango te ±. Tango 12\sqrt{2} mai i -18.

$$x=\frac{-12\sqrt{2}-18}{18}$$

Whakawehe -18-12\sqrt{2} ki te 18.

$$x=-\frac{2\sqrt{2}}{3}-1$$

Kua oti te whārite te whakatau.

$$x=\frac{2\sqrt{2}}{3}-1 x=-\frac{2\sqrt{2}}{3}-1$$

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+1\right)^{2}.

$$0=9\left(x^{2}+2x+1\right)-8$$

Whakamahia te āhuatanga tohatoha hei whakarea te 9 ki te x^{2}+2x+1.

$$0=9x^{2}+18x+9-8$$

Tangohia te 8 i te 9, ka 1.

$$0=9x^{2}+18x+1$$

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

$$9x^{2}+18x+1=0$$

Tangohia te 1 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$9x^{2}+18x=-1$$

Whakawehea ngā taha e rua ki te 9.

$$\frac{9x^{2}+18x}{9}=-\frac{1}{9}$$

Mā te whakawehe ki te 9 ka wetekia te whakareanga ki te 9.

$$x^{2}+\frac{18}{9}x=-\frac{1}{9}$$

Whakawehe 18 ki te 9.

$$x^{2}+2x=-\frac{1}{9}$$

Whakawehea te 2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 1. Nā, tāpiria te pūrua o te 1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+2x+1^{2}=-\frac{1}{9}+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=-\frac{1}{9}+1$$

Tāpiri -\frac{1}{9} ki te 1.

$$x^{2}+2x+1=\frac{8}{9}$$

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}.

$$\left(x+1\right)^{2}=\frac{8}{9}$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{\frac{8}{9}}$$

Whakarūnātia.

$$x+1=\frac{2\sqrt{2}}{3} x+1=-\frac{2\sqrt{2}}{3}$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=\frac{2\sqrt{2}}{3}-1 x=-\frac{2\sqrt{2}}{3}-1$$