Whakaoti i te (x+8)(x+8)-2=0

$$(x+8)(x+8)-2=0$$

Whakaoti mō x

$$x=\sqrt{2}-8\approx -6.585786438$$

$$x=-\left(\sqrt{2}+8\right)\approx -9.414213562$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te x+8 ki te x+8, ka \left(x+8\right)^{2}.

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

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+8\right)^{2}.

$$x^{2}+16x+64-2=0$$

Tangohia te 2 i te 64, ka 62.

$$x^{2}+16x+62=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 16 mō b, me 62 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\times 62}}{2}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\times 62}}{2}$$

Whakareatia -4 ki te 62.

$$x=\frac{-16±\sqrt{256-248}}{2}$$

Tāpiri 256 ki te -248.

$$x=\frac{-16±\sqrt{8}}{2}$$

Tuhia te pūtakerua o te 8.

$$x=\frac{-16±2\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{2}}{2} ina he tāpiri te ±. Tāpiri -16 ki te 2\sqrt{2}.

$$x=\frac{2\sqrt{2}-16}{2}$$

Whakawehe -16+2\sqrt{2} ki te 2.

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

Nā, me whakaoti te whārite x=\frac{-16±2\sqrt{2}}{2} ina he tango te ±. Tango 2\sqrt{2} mai i -16.

$$x=\frac{-2\sqrt{2}-16}{2}$$

Whakawehe -16-2\sqrt{2} ki te 2.

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

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te x+8 ki te x+8, ka \left(x+8\right)^{2}.

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

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(x+8\right)^{2}.

$$x^{2}+16x+64-2=0$$

Tangohia te 2 i te 64, ka 62.

$$x^{2}+16x+62=0$$

Tangohia te 62 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$x^{2}+16x=-62$$

Whakawehea te 16, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 8. Nā, tāpiria te pūrua o te 8 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+16x+8^{2}=-62+8^{2}$$

Pūrua 8.

$$x^{2}+16x+64=-62+64$$

Tāpiri -62 ki te 64.

$$x^{2}+16x+64=2$$

Tauwehea x^{2}+16x+64. 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}.

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

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

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

Whakarūnātia.

$$x+8=\sqrt{2} x+8=-\sqrt{2}$$

Me tango 8 mai i ngā taha e rua o te whārite.

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