Whakaoti i te (3x+2)(2x+1)=1

$$(3x+2)(2x+1)=1$$

Whakaoti mō x

$$x=-\frac{1}{6}\approx -0.166666667$$

$$x=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x+2 ki te 2x+1 ka whakakotahi i ngā kupu rite.

$$6x^{2}+7x+2=1$$

Tangohia te 1 mai i ngā taha e rua.

$$6x^{2}+7x+2-1=0$$

Tangohia te 1 i te 2, ka 1.

$$6x^{2}+7x+1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 7 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}-4\times 6}}{2\times 6}$$

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\times 6}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-7±\sqrt{49-24}}{2\times 6}$$

Tāpiri 49 ki te -24.

$$x=\frac{-7±\sqrt{25}}{2\times 6}$$

Tuhia te pūtakerua o te 25.

$$x=\frac{-7±5}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-7±5}{12}$$

Nā, me whakaoti te whārite x=\frac{-7±5}{12} ina he tāpiri te ±. Tāpiri -7 ki te 5.

$$x=-\frac{2}{12}$$

Whakahekea te hautanga \frac{-2}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{1}{6}$$

Nā, me whakaoti te whārite x=\frac{-7±5}{12} ina he tango te ±. Tango 5 mai i -7.

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

Whakawehe -12 ki te 12.

$$x=-1$$

Kua oti te whārite te whakatau.

$$x=-\frac{1}{6} x=-1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x+2 ki te 2x+1 ka whakakotahi i ngā kupu rite.

$$6x^{2}+7x+2=1$$

Tangohia te 2 mai i ngā taha e rua.

$$6x^{2}+7x=1-2$$

Tangohia te 2 i te 1, ka -1.

$$6x^{2}+7x=-1$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}+7x}{6}=-\frac{1}{6}$$

Mā te whakawehe ki te 6 ka wetekia te whakareanga ki te 6.

$$x^{2}+\frac{7}{6}x=-\frac{1}{6}$$

Whakawehea te \frac{7}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{7}{12}. Nā, tāpiria te pūrua o te \frac{7}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{7}{6}x+\left(\frac{7}{12}\right)^{2}=-\frac{1}{6}+\left(\frac{7}{12}\right)^{2}$$

Pūruatia \frac{7}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{7}{6}x+\frac{49}{144}=-\frac{1}{6}+\frac{49}{144}$$

Tāpiri -\frac{1}{6} ki te \frac{49}{144} 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.

$$x^{2}+\frac{7}{6}x+\frac{49}{144}=\frac{25}{144}$$

Tauwehea x^{2}+\frac{7}{6}x+\frac{49}{144}. 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}.

$$\left(x+\frac{7}{12}\right)^{2}=\frac{25}{144}$$

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

$$\sqrt{\left(x+\frac{7}{12}\right)^{2}}=\sqrt{\frac{25}{144}}$$

Whakarūnātia.

$$x+\frac{7}{12}=\frac{5}{12} x+\frac{7}{12}=-\frac{5}{12}$$

Me tango \frac{7}{12} mai i ngā taha e rua o te whārite.

$$x=-\frac{1}{6} x=-1$$