Whakaoti i te x*(-20x+9x)=3100

$$x \cdot ( - 20 x + 9 x ) = 3100$$

Whakaoti mō x (complex solution)

$$x=-\frac{10\sqrt{341}i}{11}\approx -0-16.787441193i$$

$$x=\frac{10\sqrt{341}i}{11}\approx 16.787441193i$$

Ngā Upane mā te Kimi Pūtakerua

Pahekotia te -20x me 9x, ka -11x.

$$x\left(-11\right)x=3100$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}\left(-11\right)=3100$$

Whakawehea ngā taha e rua ki te -11.

$$x^{2}=-\frac{3100}{11}$$

Kua oti te whārite te whakatau.

$$x=\frac{10\sqrt{341}i}{11} x=-\frac{10\sqrt{341}i}{11}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te -20x me 9x, ka -11x.

$$x\left(-11\right)x=3100$$

Whakareatia te x ki te x, ka x^{2}.

$$x^{2}\left(-11\right)=3100$$

Tangohia te 3100 mai i ngā taha e rua.

$$x^{2}\left(-11\right)-3100=0$$

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.

$$-11x^{2}-3100=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -11 mō a, 0 mō b, me -3100 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-11\right)\left(-3100\right)}}{2\left(-11\right)}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-11\right)\left(-3100\right)}}{2\left(-11\right)}$$

Whakareatia -4 ki te -11.

$$x=\frac{0±\sqrt{44\left(-3100\right)}}{2\left(-11\right)}$$

Whakareatia 44 ki te -3100.

$$x=\frac{0±\sqrt{-136400}}{2\left(-11\right)}$$

Tuhia te pūtakerua o te -136400.

$$x=\frac{0±20\sqrt{341}i}{2\left(-11\right)}$$

Whakareatia 2 ki te -11.

$$x=\frac{0±20\sqrt{341}i}{-22}$$

Nā, me whakaoti te whārite x=\frac{0±20\sqrt{341}i}{-22} ina he tāpiri te ±.

$$x=-\frac{10\sqrt{341}i}{11}$$

Nā, me whakaoti te whārite x=\frac{0±20\sqrt{341}i}{-22} ina he tango te ±.

$$x=\frac{10\sqrt{341}i}{11}$$

Kua oti te whārite te whakatau.

$$x=-\frac{10\sqrt{341}i}{11} x=\frac{10\sqrt{341}i}{11}$$