Whakaoti i te x*(x+x)=7

$$x \times (x+x)=7$$

Whakaoti mō x

$$x = \frac{\sqrt{14}}{2} \approx 1.870828693$$

$$x = -\frac{\sqrt{14}}{2} \approx -1.870828693$$

Ngā Upane mā te Kimi Pūtakerua

Pahekotia te x me x, ka 2x.

$$x\times 2x=7$$

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

$$x^{2}\times 2=7$$

Whakawehea ngā taha e rua ki te 2.

$$x^{2}=\frac{7}{2}$$

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

$$x=\frac{\sqrt{14}}{2} x=-\frac{\sqrt{14}}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te x me x, ka 2x.

$$x\times 2x=7$$

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

$$x^{2}\times 2=7$$

Tangohia te 7 mai i ngā taha e rua.

$$x^{2}\times 2-7=0$$

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.

$$2x^{2}-7=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me -7 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-7\right)}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-7\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\left(-7\right)}}{2\times 2}$$

Whakareatia -8 ki te -7.

$$x=\frac{0±\sqrt{56}}{2\times 2}$$

Tuhia te pūtakerua o te 56.

$$x=\frac{0±2\sqrt{14}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±2\sqrt{14}}{4}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{14}}{4} ina he tāpiri te ±.

$$x=\frac{\sqrt{14}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{14}}{4} ina he tango te ±.

$$x=-\frac{\sqrt{14}}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{14}}{2} x=-\frac{\sqrt{14}}{2}$$