Whakaoti i te 2x^2=(8-x)^2

$$2 x ^ { 2 } = ( 8 - x ) ^ { 2 }$$

Whakaoti mō x

$$x=8\sqrt{2}-8\approx 3.313708499$$

$$x=-8\sqrt{2}-8\approx -19.313708499$$

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(8-x\right)^{2}.

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

Tangohia te 64 mai i ngā taha e rua.

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

Me tāpiri te 16x ki ngā taha e rua.

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

Tangohia te x^{2} mai i ngā taha e rua.

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

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

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

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 16 mō b, me -64 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\left(-64\right)}}{2}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\left(-64\right)}}{2}$$

Whakareatia -4 ki te -64.

$$x=\frac{-16±\sqrt{256+256}}{2}$$

Tāpiri 256 ki te 256.

$$x=\frac{-16±\sqrt{512}}{2}$$

Tuhia te pūtakerua o te 512.

$$x=\frac{-16±16\sqrt{2}}{2}$$

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

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

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

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

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

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

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

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

Kua oti te whārite te whakatau.

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

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(8-x\right)^{2}.

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

Me tāpiri te 16x ki ngā taha e rua.

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

Tangohia te x^{2} mai i ngā taha e rua.

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

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

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

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.

$$x^{2}+16x+8^{2}=64+8^{2}$$

Pūrua 8.

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

Tāpiri 64 ki te 64.

$$x^{2}+16x+64=128$$

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}.

$$\left(x+8\right)^{2}=128$$

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

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{128}$$

Whakarūnātia.

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

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

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