Whakaoti i te 3x(2x-1)+8x=1

$$3 x ( 2 x - 1 ) + 8 x = 1$$

Whakaoti mō x

$$x=-1$$

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 3x ki te 2x-1.

$$6x^{2}-3x+8x=1$$

Pahekotia te -3x me 8x, ka 5x.

$$6x^{2}+5x=1$$

Tangohia te 1 mai i ngā taha e rua.

$$6x^{2}+5x-1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 5 mō b, me -1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\times 6\left(-1\right)}}{2\times 6}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\times 6\left(-1\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-5±\sqrt{25-24\left(-1\right)}}{2\times 6}$$

Whakareatia -24 ki te -1.

$$x=\frac{-5±\sqrt{25+24}}{2\times 6}$$

Tāpiri 25 ki te 24.

$$x=\frac{-5±\sqrt{49}}{2\times 6}$$

Tuhia te pūtakerua o te 49.

$$x=\frac{-5±7}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-5±7}{12}$$

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

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

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{-5±7}{12} ina he tango te ±. Tango 7 mai i -5.

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

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 tohatoha hei whakarea te 3x ki te 2x-1.

$$6x^{2}-3x+8x=1$$

Pahekotia te -3x me 8x, ka 5x.

$$6x^{2}+5x=1$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}+5x}{6}=\frac{1}{6}$$

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

$$x^{2}+\frac{5}{6}x=\frac{1}{6}$$

Whakawehea te \frac{5}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{12}. Nā, tāpiria te pūrua o te \frac{5}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{5}{6}x+\left(\frac{5}{12}\right)^{2}=\frac{1}{6}+\left(\frac{5}{12}\right)^{2}$$

Pūruatia \frac{5}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{5}{6}x+\frac{25}{144}=\frac{1}{6}+\frac{25}{144}$$

Tāpiri \frac{1}{6} ki te \frac{25}{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.

$$x^{2}+\frac{5}{6}x+\frac{25}{144}=\frac{49}{144}$$

Tauwehea x^{2}+\frac{5}{6}x+\frac{25}{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}.

$$\left(x+\frac{5}{12}\right)^{2}=\frac{49}{144}$$

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

$$\sqrt{\left(x+\frac{5}{12}\right)^{2}}=\sqrt{\frac{49}{144}}$$

Whakarūnātia.

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

Me tango \frac{5}{12} mai i ngā taha e rua o te whārite.

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