Whakaoti i te 2x(x-3)=x-3

$$2x(x-3)=x-3$$

Whakaoti mō x

$$x=\frac{1}{2}=0.5$$

$$x=3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-3.

$$2x^{2}-6x=x-3$$

Tangohia te x mai i ngā taha e rua.

$$2x^{2}-6x-x=-3$$

Pahekotia te -6x me -x, ka -7x.

$$2x^{2}-7x=-3$$

Me tāpiri te 3 ki ngā taha e rua.

$$2x^{2}-7x+3=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -7 mō b, me 3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 2\times 3}}{2\times 2}$$

Pūrua -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\times 2\times 3}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-7\right)±\sqrt{49-8\times 3}}{2\times 2}$$

Whakareatia -8 ki te 3.

$$x=\frac{-\left(-7\right)±\sqrt{49-24}}{2\times 2}$$

Tāpiri 49 ki te -24.

$$x=\frac{-\left(-7\right)±\sqrt{25}}{2\times 2}$$

Tuhia te pūtakerua o te 25.

$$x=\frac{-\left(-7\right)±5}{2\times 2}$$

Ko te tauaro o -7 ko 7.

$$x=\frac{7±5}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{7±5}{4}$$

Nā, me whakaoti te whārite x=\frac{7±5}{4} ina he tāpiri te ±. Tāpiri 7 ki te 5.

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

Whakawehe 12 ki te 4.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{7±5}{4} ina he tango te ±. Tango 5 mai i 7.

$$x=\frac{2}{4}$$

Whakahekea te hautanga \frac{2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{1}{2}$$

Kua oti te whārite te whakatau.

$$x=3 x=\frac{1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te x-3.

$$2x^{2}-6x=x-3$$

Tangohia te x mai i ngā taha e rua.

$$2x^{2}-6x-x=-3$$

Pahekotia te -6x me -x, ka -7x.

$$2x^{2}-7x=-3$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-7x}{2}=-\frac{3}{2}$$

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

$$x^{2}-\frac{7}{2}x=-\frac{3}{2}$$

Whakawehea te -\frac{7}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{4}. Nā, tāpiria te pūrua o te -\frac{7}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{7}{2}x+\left(-\frac{7}{4}\right)^{2}=-\frac{3}{2}+\left(-\frac{7}{4}\right)^{2}$$

Pūruatia -\frac{7}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=-\frac{3}{2}+\frac{49}{16}$$

Tāpiri -\frac{3}{2} ki te \frac{49}{16} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=\frac{25}{16}$$

Tauwehea x^{2}-\frac{7}{2}x+\frac{49}{16}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{4}\right)^{2}=\frac{25}{16}$$

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

$$\sqrt{\left(x-\frac{7}{4}\right)^{2}}=\sqrt{\frac{25}{16}}$$

Whakarūnātia.

$$x-\frac{7}{4}=\frac{5}{4} x-\frac{7}{4}=-\frac{5}{4}$$

Me tāpiri \frac{7}{4} ki ngā taha e rua o te whārite.

$$x=3 x=\frac{1}{2}$$