Whakaoti i te 6^2-x^2=2*25*4

$$6 ^ { 2 } - x ^ { 2 } = 2 \times 25 \times 4$$

Whakaoti mō x (complex solution)

$$x=-2\sqrt{41}i\approx -0-12.806248475i$$

$$x=2\sqrt{41}i\approx 12.806248475i$$

Ngā Upane mā te Kimi Pūtakerua

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$36-x^{2}=2\times 25\times 4$$

Whakareatia te 2 ki te 25, ka 50.

$$36-x^{2}=50\times 4$$

Whakareatia te 50 ki te 4, ka 200.

$$36-x^{2}=200$$

Tangohia te 36 mai i ngā taha e rua.

$$-x^{2}=200-36$$

Tangohia te 36 i te 200, ka 164.

$$-x^{2}=164$$

Whakawehea ngā taha e rua ki te -1.

$$x^{2}=-164$$

Kua oti te whārite te whakatau.

$$x=2\sqrt{41}i x=-2\sqrt{41}i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tātaihia te 6 mā te pū o 2, kia riro ko 36.

$$36-x^{2}=2\times 25\times 4$$

Whakareatia te 2 ki te 25, ka 50.

$$36-x^{2}=50\times 4$$

Whakareatia te 50 ki te 4, ka 200.

$$36-x^{2}=200$$

Tangohia te 200 mai i ngā taha e rua.

$$36-x^{2}-200=0$$

Tangohia te 200 i te 36, ka -164.

$$-164-x^{2}=0$$

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.

$$-x^{2}-164=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 0 mō b, me -164 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-164\right)}}{2\left(-1\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-164\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{0±\sqrt{4\left(-164\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -164.

$$x=\frac{0±\sqrt{-656}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te -656.

$$x=\frac{0±4\sqrt{41}i}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{0±4\sqrt{41}i}{-2}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{41}i}{-2} ina he tāpiri te ±.

$$x=-2\sqrt{41}i$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{41}i}{-2} ina he tango te ±.

$$x=2\sqrt{41}i$$

Kua oti te whārite te whakatau.

$$x=-2\sqrt{41}i x=2\sqrt{41}i$$