Whakaoti i te 2x(3x-4)=5x

$$2x(3x-4)=5x$$

Whakaoti mō x

$$x = \frac{13}{6} = 2\frac{1}{6} \approx 2.166666667$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te 3x-4.

$$6x^{2}-8x=5x$$

Tangohia te 5x mai i ngā taha e rua.

$$6x^{2}-8x-5x=0$$

Pahekotia te -8x me -5x, ka -13x.

$$6x^{2}-13x=0$$

Tauwehea te x.

$$x\left(6x-13\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 6x-13=0.

$$x=0 x=\frac{13}{6}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te 3x-4.

$$6x^{2}-8x=5x$$

Tangohia te 5x mai i ngā taha e rua.

$$6x^{2}-8x-5x=0$$

Pahekotia te -8x me -5x, ka -13x.

$$6x^{2}-13x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, -13 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}}}{2\times 6}$$

Tuhia te pūtakerua o te \left(-13\right)^{2}.

$$x=\frac{-\left(-13\right)±13}{2\times 6}$$

Ko te tauaro o -13 ko 13.

$$x=\frac{13±13}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{13±13}{12}$$

Nā, me whakaoti te whārite x=\frac{13±13}{12} ina he tāpiri te ±. Tāpiri 13 ki te 13.

$$x=\frac{26}{12}$$

Whakahekea te hautanga \frac{26}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{13}{6}$$

Nā, me whakaoti te whārite x=\frac{13±13}{12} ina he tango te ±. Tango 13 mai i 13.

$$x=\frac{0}{12}$$

Whakawehe 0 ki te 12.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{13}{6} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2x ki te 3x-4.

$$6x^{2}-8x=5x$$

Tangohia te 5x mai i ngā taha e rua.

$$6x^{2}-8x-5x=0$$

Pahekotia te -8x me -5x, ka -13x.

$$6x^{2}-13x=0$$

Whakawehea ngā taha e rua ki te 6.

$$\frac{6x^{2}-13x}{6}=\frac{0}{6}$$

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

$$x^{2}-\frac{13}{6}x=\frac{0}{6}$$

Whakawehe 0 ki te 6.

$$x^{2}-\frac{13}{6}x=0$$

Whakawehea te -\frac{13}{6}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{13}{12}. Nā, tāpiria te pūrua o te -\frac{13}{12} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{13}{6}x+\left(-\frac{13}{12}\right)^{2}=\left(-\frac{13}{12}\right)^{2}$$

Pūruatia -\frac{13}{12} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{13}{6}x+\frac{169}{144}=\frac{169}{144}$$

Tauwehea x^{2}-\frac{13}{6}x+\frac{169}{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}.

$$\left(x-\frac{13}{12}\right)^{2}=\frac{169}{144}$$

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

$$\sqrt{\left(x-\frac{13}{12}\right)^{2}}=\sqrt{\frac{169}{144}}$$

Whakarūnātia.

$$x-\frac{13}{12}=\frac{13}{12} x-\frac{13}{12}=-\frac{13}{12}$$

Me tāpiri \frac{13}{12} ki ngā taha e rua o te whārite.

$$x=\frac{13}{6} x=0$$