Whakaoti i te 256=96x-16x^2+256

$$256 = 96x-16 { x }^{ 2 } +256$$

Whakaoti mō x

$$x=6$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

$$96x-16x^{2}+256=256$$

Tangohia te 256 mai i ngā taha e rua.

$$96x-16x^{2}+256-256=0$$

Tangohia te 256 i te 256, ka 0.

$$96x-16x^{2}=0$$

Tauwehea te x.

$$x\left(96-16x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 96-16x=0.

$$x=0 x=6$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$96x-16x^{2}+256=256$$

Tangohia te 256 mai i ngā taha e rua.

$$96x-16x^{2}+256-256=0$$

Tangohia te 256 i te 256, ka 0.

$$96x-16x^{2}=0$$

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.

$$-16x^{2}+96x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -16 mō a, 96 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-96±\sqrt{96^{2}}}{2\left(-16\right)}$$

Tuhia te pūtakerua o te 96^{2}.

$$x=\frac{-96±96}{2\left(-16\right)}$$

Whakareatia 2 ki te -16.

$$x=\frac{-96±96}{-32}$$

Nā, me whakaoti te whārite x=\frac{-96±96}{-32} ina he tāpiri te ±. Tāpiri -96 ki te 96.

$$x=\frac{0}{-32}$$

Whakawehe 0 ki te -32.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-96±96}{-32} ina he tango te ±. Tango 96 mai i -96.

$$x=-\frac{192}{-32}$$

Whakawehe -192 ki te -32.

$$x=6$$

Kua oti te whārite te whakatau.

$$x=0 x=6$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$96x-16x^{2}+256=256$$

Tangohia te 256 mai i ngā taha e rua.

$$96x-16x^{2}=256-256$$

Tangohia te 256 i te 256, ka 0.

$$96x-16x^{2}=0$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-16x^{2}+96x=0$$

Whakawehea ngā taha e rua ki te -16.

$$\frac{-16x^{2}+96x}{-16}=\frac{0}{-16}$$

Mā te whakawehe ki te -16 ka wetekia te whakareanga ki te -16.

$$x^{2}+\frac{96}{-16}x=\frac{0}{-16}$$

Whakawehe 96 ki te -16.

$$x^{2}-6x=\frac{0}{-16}$$

Whakawehe 0 ki te -16.

$$x^{2}-6x=0$$

Whakawehea te -6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -3. Nā, tāpiria te pūrua o te -3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-6x+\left(-3\right)^{2}=\left(-3\right)^{2}$$

Pūrua -3.

$$x^{2}-6x+9=9$$

Tauwehea x^{2}-6x+9. 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}.

$$\left(x-3\right)^{2}=9$$

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

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{9}$$

Whakarūnātia.

$$x-3=3 x-3=-3$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$x=6 x=0$$