Whakaoti i te x^2+x(x-6)=0

$$x ^ { 2 } + x ( x - 6 ) = 0$$

Whakaoti mō x

$$x=3$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-6.

$$x^{2}+x^{2}-6x=0$$

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$2x^{2}-6x=0$$

Tauwehea te x.

$$x\left(2x-6\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 2x-6=0.

$$x=0 x=3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-6.

$$x^{2}+x^{2}-6x=0$$

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$2x^{2}-6x=0$$

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

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\times 2}$$

Tuhia te pūtakerua o te \left(-6\right)^{2}.

$$x=\frac{-\left(-6\right)±6}{2\times 2}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±6}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{6±6}{4}$$

Nā, me whakaoti te whārite x=\frac{6±6}{4} ina he tāpiri te ±. Tāpiri 6 ki te 6.

$$x=\frac{12}{4}$$

Whakawehe 12 ki te 4.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{6±6}{4} ina he tango te ±. Tango 6 mai i 6.

$$x=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=3 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-6.

$$x^{2}+x^{2}-6x=0$$

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

$$2x^{2}-6x=0$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-6x}{2}=\frac{0}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\left(-\frac{6}{2}\right)x=\frac{0}{2}$$

Whakawehe -6 ki te 2.

$$x^{2}-3x=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$x^{2}-3x=0$$

Whakawehea te -3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{2}. Nā, tāpiria te pūrua o te -\frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=\left(-\frac{3}{2}\right)^{2}$$

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3x+\frac{9}{4}=\frac{9}{4}$$

Tauwehea te x^{2}-3x+\frac{9}{4}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

$$x-\frac{3}{2}=\frac{3}{2} x-\frac{3}{2}=-\frac{3}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$x=3 x=0$$