Whakaoti i te 96-2z^2-4z^2=0

$$96 - 2 z ^ { 2 } - 4 z ^ { 2 } = 0$$

Whakaoti mō z

$$z=4$$

$$z=-4$$

Ngā Upane mā te Kimi Pūtakerua

Pahekotia te -2z^{2} me -4z^{2}, ka -6z^{2}.

$$96-6z^{2}=0$$

Tangohia te 96 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-6z^{2}=-96$$

Whakawehea ngā taha e rua ki te -6.

$$z^{2}=\frac{-96}{-6}$$

Whakawehea te -96 ki te -6, kia riro ko 16.

$$z^{2}=16$$

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

$$z=4 z=-4$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te -2z^{2} me -4z^{2}, ka -6z^{2}.

$$96-6z^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-6z^{2}+96=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -6 mō a, 0 mō b, me 96 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-6\right)\times 96}}{2\left(-6\right)}$$

Pūrua 0.

$$z=\frac{0±\sqrt{-4\left(-6\right)\times 96}}{2\left(-6\right)}$$

Whakareatia -4 ki te -6.

$$z=\frac{0±\sqrt{24\times 96}}{2\left(-6\right)}$$

Whakareatia 24 ki te 96.

$$z=\frac{0±\sqrt{2304}}{2\left(-6\right)}$$

Tuhia te pūtakerua o te 2304.

$$z=\frac{0±48}{2\left(-6\right)}$$

Whakareatia 2 ki te -6.

$$z=\frac{0±48}{-12}$$

Nā, me whakaoti te whārite z=\frac{0±48}{-12} ina he tāpiri te ±. Whakawehe 48 ki te -12.

$$z=-4$$

Nā, me whakaoti te whārite z=\frac{0±48}{-12} ina he tango te ±. Whakawehe -48 ki te -12.

$$z=4$$

Kua oti te whārite te whakatau.

$$z=-4 z=4$$