Whakaoti i te -7x(x-1)=(x-1)(x+1)

$$-7x(x-1)=(x-1)(x+1)$$

Whakaoti mō x

$$x=1$$

$$x=-\frac{1}{8}=-0.125$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te -7x ki te x-1.

$$-7x^{2}+7x=\left(x-1\right)\left(x+1\right)$$

Whakaarohia te \left(x-1\right)\left(x+1\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 1.

$$-7x^{2}+7x=x^{2}-1$$

Tangohia te x^{2} mai i ngā taha e rua.

$$-7x^{2}+7x-x^{2}=-1$$

Pahekotia te -7x^{2} me -x^{2}, ka -8x^{2}.

$$-8x^{2}+7x=-1$$

Me tāpiri te 1 ki ngā taha e rua.

$$-8x^{2}+7x+1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -8 mō a, 7 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-8\right)}}{2\left(-8\right)}$$

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\left(-8\right)}}{2\left(-8\right)}$$

Whakareatia -4 ki te -8.

$$x=\frac{-7±\sqrt{49+32}}{2\left(-8\right)}$$

Tāpiri 49 ki te 32.

$$x=\frac{-7±\sqrt{81}}{2\left(-8\right)}$$

Tuhia te pūtakerua o te 81.

$$x=\frac{-7±9}{2\left(-8\right)}$$

Whakareatia 2 ki te -8.

$$x=\frac{-7±9}{-16}$$

Nā, me whakaoti te whārite x=\frac{-7±9}{-16} ina he tāpiri te ±. Tāpiri -7 ki te 9.

$$x=\frac{2}{-16}$$

Whakahekea te hautanga \frac{2}{-16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{1}{8}$$

Nā, me whakaoti te whārite x=\frac{-7±9}{-16} ina he tango te ±. Tango 9 mai i -7.

$$x=-\frac{16}{-16}$$

Whakawehe -16 ki te -16.

$$x=1$$

Kua oti te whārite te whakatau.

$$x=-\frac{1}{8} x=1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te -7x ki te x-1.

$$-7x^{2}+7x=\left(x-1\right)\left(x+1\right)$$

Whakaarohia te \left(x-1\right)\left(x+1\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 1.

$$-7x^{2}+7x=x^{2}-1$$

Tangohia te x^{2} mai i ngā taha e rua.

$$-7x^{2}+7x-x^{2}=-1$$

Pahekotia te -7x^{2} me -x^{2}, ka -8x^{2}.

$$-8x^{2}+7x=-1$$

Whakawehea ngā taha e rua ki te -8.

$$\frac{-8x^{2}+7x}{-8}=-\frac{1}{-8}$$

Mā te whakawehe ki te -8 ka wetekia te whakareanga ki te -8.

$$x^{2}+\frac{7}{-8}x=-\frac{1}{-8}$$

Whakawehe 7 ki te -8.

$$x^{2}-\frac{7}{8}x=-\frac{1}{-8}$$

Whakawehe -1 ki te -8.

$$x^{2}-\frac{7}{8}x=\frac{1}{8}$$

Whakawehea te -\frac{7}{8}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{16}. Nā, tāpiria te pūrua o te -\frac{7}{16} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{7}{8}x+\left(-\frac{7}{16}\right)^{2}=\frac{1}{8}+\left(-\frac{7}{16}\right)^{2}$$

Pūruatia -\frac{7}{16} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{7}{8}x+\frac{49}{256}=\frac{1}{8}+\frac{49}{256}$$

Tāpiri \frac{1}{8} ki te \frac{49}{256} 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.

$$x^{2}-\frac{7}{8}x+\frac{49}{256}=\frac{81}{256}$$

Tauwehea x^{2}-\frac{7}{8}x+\frac{49}{256}. 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}.

$$\left(x-\frac{7}{16}\right)^{2}=\frac{81}{256}$$

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

$$\sqrt{\left(x-\frac{7}{16}\right)^{2}}=\sqrt{\frac{81}{256}}$$

Whakarūnātia.

$$x-\frac{7}{16}=\frac{9}{16} x-\frac{7}{16}=-\frac{9}{16}$$

Me tāpiri \frac{7}{16} ki ngā taha e rua o te whārite.

$$x=1 x=-\frac{1}{8}$$