Whakaoti i te x^2-34=16x

$${ x }^{ 2 } -34=16x$$

Whakaoti mō x

$$x=7\sqrt{2}+8\approx 17.899494937$$

$$x=8-7\sqrt{2}\approx -1.899494937$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 16x mai i ngā taha e rua.

$$x^{2}-34-16x=0$$

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.

$$x^{2}-16x-34=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -16 mō b, me -34 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-34\right)}}{2}$$

Pūrua -16.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\left(-34\right)}}{2}$$

Whakareatia -4 ki te -34.

$$x=\frac{-\left(-16\right)±\sqrt{256+136}}{2}$$

Tāpiri 256 ki te 136.

$$x=\frac{-\left(-16\right)±\sqrt{392}}{2}$$

Tuhia te pūtakerua o te 392.

$$x=\frac{-\left(-16\right)±14\sqrt{2}}{2}$$

Ko te tauaro o -16 ko 16.

$$x=\frac{16±14\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{16±14\sqrt{2}}{2} ina he tāpiri te ±. Tāpiri 16 ki te 14\sqrt{2}.

$$x=\frac{14\sqrt{2}+16}{2}$$

Whakawehe 16+14\sqrt{2} ki te 2.

$$x=7\sqrt{2}+8$$

Nā, me whakaoti te whārite x=\frac{16±14\sqrt{2}}{2} ina he tango te ±. Tango 14\sqrt{2} mai i 16.

$$x=\frac{16-14\sqrt{2}}{2}$$

Whakawehe 16-14\sqrt{2} ki te 2.

$$x=8-7\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=7\sqrt{2}+8 x=8-7\sqrt{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 16x mai i ngā taha e rua.

$$x^{2}-34-16x=0$$

Me tāpiri te 34 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$x^{2}-16x=34$$

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.

$$x^{2}-16x+\left(-8\right)^{2}=34+\left(-8\right)^{2}$$

Pūrua -8.

$$x^{2}-16x+64=34+64$$

Tāpiri 34 ki te 64.

$$x^{2}-16x+64=98$$

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}.

$$\left(x-8\right)^{2}=98$$

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

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{98}$$

Whakarūnātia.

$$x-8=7\sqrt{2} x-8=-7\sqrt{2}$$

Me tāpiri 8 ki ngā taha e rua o te whārite.

$$x=7\sqrt{2}+8 x=8-7\sqrt{2}$$