Whakaoti i te (2x-3)(4x-1)=3

$$( 2 x - 3 ) ( 4 x - 1 ) = 3$$

Whakaoti mō x

$$x = \frac{7}{4} = 1\frac{3}{4} = 1.75$$

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-3 ki te 4x-1 ka whakakotahi i ngā kupu rite.

$$8x^{2}-14x+3=3$$

Tangohia te 3 mai i ngā taha e rua.

$$8x^{2}-14x+3-3=0$$

Tangohia te 3 i te 3, ka 0.

$$8x^{2}-14x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, -14 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}}}{2\times 8}$$

Tuhia te pūtakerua o te \left(-14\right)^{2}.

$$x=\frac{-\left(-14\right)±14}{2\times 8}$$

Ko te tauaro o -14 ko 14.

$$x=\frac{14±14}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{14±14}{16}$$

Nā, me whakaoti te whārite x=\frac{14±14}{16} ina he tāpiri te ±. Tāpiri 14 ki te 14.

$$x=\frac{28}{16}$$

Whakahekea te hautanga \frac{28}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{7}{4}$$

Nā, me whakaoti te whārite x=\frac{14±14}{16} ina he tango te ±. Tango 14 mai i 14.

$$x=\frac{0}{16}$$

Whakawehe 0 ki te 16.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{7}{4} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 2x-3 ki te 4x-1 ka whakakotahi i ngā kupu rite.

$$8x^{2}-14x+3=3$$

Tangohia te 3 mai i ngā taha e rua.

$$8x^{2}-14x=3-3$$

Tangohia te 3 i te 3, ka 0.

$$8x^{2}-14x=0$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8x^{2}-14x}{8}=\frac{0}{8}$$

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

$$x^{2}+\left(-\frac{14}{8}\right)x=\frac{0}{8}$$

Whakahekea te hautanga \frac{-14}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{7}{4}x=\frac{0}{8}$$

Whakawehe 0 ki te 8.

$$x^{2}-\frac{7}{4}x=0$$

Whakawehea te -\frac{7}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{8}. Nā, tāpiria te pūrua o te -\frac{7}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūruatia -\frac{7}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{7}{4}x+\frac{49}{64}=\frac{49}{64}$$

Tauwehea x^{2}-\frac{7}{4}x+\frac{49}{64}. 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}.

$$\left(x-\frac{7}{8}\right)^{2}=\frac{49}{64}$$

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

$$\sqrt{\left(x-\frac{7}{8}\right)^{2}}=\sqrt{\frac{49}{64}}$$

Whakarūnātia.

$$x-\frac{7}{8}=\frac{7}{8} x-\frac{7}{8}=-\frac{7}{8}$$

Me tāpiri \frac{7}{8} ki ngā taha e rua o te whārite.

$$x=\frac{7}{4} x=0$$