Whakaoti i te -4x(x-1)=2x-2

$$-4x(x-1)=2x-2$$

Whakaoti mō x

$$x=1$$

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te -4x ki te x-1.

$$-4x^{2}+4x=2x-2$$

Tangohia te 2x mai i ngā taha e rua.

$$-4x^{2}+4x-2x=-2$$

Pahekotia te 4x me -2x, ka 2x.

$$-4x^{2}+2x=-2$$

Me tāpiri te 2 ki ngā taha e rua.

$$-4x^{2}+2x+2=0$$

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

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

Pūrua 2.

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

Whakareatia -4 ki te -4.

$$x=\frac{-2±\sqrt{4+16\times 2}}{2\left(-4\right)}$$

Whakareatia 16 ki te 2.

$$x=\frac{-2±\sqrt{4+32}}{2\left(-4\right)}$$

Tāpiri 4 ki te 32.

$$x=\frac{-2±\sqrt{36}}{2\left(-4\right)}$$

Tuhia te pūtakerua o te 36.

$$x=\frac{-2±6}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{-2±6}{-8}$$

Nā, me whakaoti te whārite x=\frac{-2±6}{-8} ina he tāpiri te ±. Tāpiri -2 ki te 6.

$$x=\frac{4}{-8}$$

Whakahekea te hautanga \frac{4}{-8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Nā, me whakaoti te whārite x=\frac{-2±6}{-8} ina he tango te ±. Tango 6 mai i -2.

$$x=-\frac{8}{-8}$$

Whakawehe -8 ki te -8.

$$x=1$$

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te -4x ki te x-1.

$$-4x^{2}+4x=2x-2$$

Tangohia te 2x mai i ngā taha e rua.

$$-4x^{2}+4x-2x=-2$$

Pahekotia te 4x me -2x, ka 2x.

$$-4x^{2}+2x=-2$$

Whakawehea ngā taha e rua ki te -4.

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

Mā te whakawehe ki te -4 ka wetekia te whakareanga ki te -4.

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

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

$$x^{2}-\frac{1}{2}x=-\frac{2}{-4}$$

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

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

Whakawehea te -\frac{1}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{4}. Nā, tāpiria te pūrua o te -\frac{1}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{2}x+\left(-\frac{1}{4}\right)^{2}=\frac{1}{2}+\left(-\frac{1}{4}\right)^{2}$$

Pūruatia -\frac{1}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{1}{2}+\frac{1}{16}$$

Tāpiri \frac{1}{2} ki te \frac{1}{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.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{9}{16}$$

Tauwehea x^{2}-\frac{1}{2}x+\frac{1}{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}.

$$\left(x-\frac{1}{4}\right)^{2}=\frac{9}{16}$$

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

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{9}{16}}$$

Whakarūnātia.

$$x-\frac{1}{4}=\frac{3}{4} x-\frac{1}{4}=-\frac{3}{4}$$

Me tāpiri \frac{1}{4} ki ngā taha e rua o te whārite.

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