Whakaoti i te z^2-25*10^-12+16*10^-12=0

$${ z }^{ 2 } -25 \times { 10 }^{ -12 } +16 \times { 10 }^{ -12 } = 0$$

Whakaoti mō z

$$z=\frac{3}{1000000}=0.000003$$

$$z=-\frac{3}{1000000}=-0.000003$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 10 mā te pū o -12, kia riro ko \frac{1}{1000000000000}.

$$z^{2}-25\times \frac{1}{1000000000000}+16\times 10^{-12}=0$$

Whakareatia te 25 ki te \frac{1}{1000000000000}, ka \frac{1}{40000000000}.

$$z^{2}-\frac{1}{40000000000}+16\times 10^{-12}=0$$

Tātaihia te 10 mā te pū o -12, kia riro ko \frac{1}{1000000000000}.

$$z^{2}-\frac{1}{40000000000}+16\times \frac{1}{1000000000000}=0$$

Whakareatia te 16 ki te \frac{1}{1000000000000}, ka \frac{1}{62500000000}.

$$z^{2}-\frac{1}{40000000000}+\frac{1}{62500000000}=0$$

Tāpirihia te -\frac{1}{40000000000} ki te \frac{1}{62500000000}, ka -\frac{9}{1000000000000}.

$$z^{2}-\frac{9}{1000000000000}=0$$

Me tāpiri te \frac{9}{1000000000000} ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$z^{2}=\frac{9}{1000000000000}$$

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

$$z=\frac{3}{1000000} z=-\frac{3}{1000000}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 10 mā te pū o -12, kia riro ko \frac{1}{1000000000000}.

$$z^{2}-25\times \frac{1}{1000000000000}+16\times 10^{-12}=0$$

Whakareatia te 25 ki te \frac{1}{1000000000000}, ka \frac{1}{40000000000}.

$$z^{2}-\frac{1}{40000000000}+16\times 10^{-12}=0$$

Tātaihia te 10 mā te pū o -12, kia riro ko \frac{1}{1000000000000}.

$$z^{2}-\frac{1}{40000000000}+16\times \frac{1}{1000000000000}=0$$

Whakareatia te 16 ki te \frac{1}{1000000000000}, ka \frac{1}{62500000000}.

$$z^{2}-\frac{1}{40000000000}+\frac{1}{62500000000}=0$$

Tāpirihia te -\frac{1}{40000000000} ki te \frac{1}{62500000000}, ka -\frac{9}{1000000000000}.

$$z^{2}-\frac{9}{1000000000000}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -\frac{9}{1000000000000} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{1000000000000}\right)}}{2}$$

Pūrua 0.

$$z=\frac{0±\sqrt{-4\left(-\frac{9}{1000000000000}\right)}}{2}$$

Whakareatia -4 ki te -\frac{9}{1000000000000}.

$$z=\frac{0±\sqrt{\frac{9}{250000000000}}}{2}$$

Tuhia te pūtakerua o te \frac{9}{250000000000}.

$$z=\frac{0±\frac{3}{500000}}{2}$$

Nā, me whakaoti te whārite z=\frac{0±\frac{3}{500000}}{2} ina he tāpiri te ±.

$$z=\frac{3}{1000000}$$

Nā, me whakaoti te whārite z=\frac{0±\frac{3}{500000}}{2} ina he tango te ±.

$$z=-\frac{3}{1000000}$$

Kua oti te whārite te whakatau.

$$z=\frac{3}{1000000} z=-\frac{3}{1000000}$$