Whakaoti i te 4x^2-3x=0

$$4 x ^ { 2 } - 3 x = 0$$

Whakaoti mō x

$$x=\frac{3}{4}=0.75$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(4x-3\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 4x-3=0.

$$x=0 x=\frac{3}{4}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$4x^{2}-3x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, -3 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\times 4}$$

Tuhia te pūtakerua o te \left(-3\right)^{2}.

$$x=\frac{-\left(-3\right)±3}{2\times 4}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±3}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{3±3}{8}$$

Nā, me whakaoti te whārite x=\frac{3±3}{8} ina he tāpiri te ±. Tāpiri 3 ki te 3.

$$x=\frac{6}{8}$$

Whakahekea te hautanga \frac{6}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{3}{4}$$

Nā, me whakaoti te whārite x=\frac{3±3}{8} ina he tango te ±. Tango 3 mai i 3.

$$x=\frac{0}{8}$$

Whakawehe 0 ki te 8.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{3}{4} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$4x^{2}-3x=0$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}-3x}{4}=\frac{0}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$x^{2}-\frac{3}{4}x=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$x^{2}-\frac{3}{4}x=0$$

Whakawehea te -\frac{3}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{8}. Nā, tāpiria te pūrua o te -\frac{3}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{3}{4}x+\left(-\frac{3}{8}\right)^{2}=\left(-\frac{3}{8}\right)^{2}$$

Pūruatia -\frac{3}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{3}{4}x+\frac{9}{64}=\frac{9}{64}$$

Tauwehea te x^{2}-\frac{3}{4}x+\frac{9}{64}. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{3}{8}\right)^{2}=\frac{9}{64}$$

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

$$\sqrt{\left(x-\frac{3}{8}\right)^{2}}=\sqrt{\frac{9}{64}}$$

Whakarūnātia.

$$x-\frac{3}{8}=\frac{3}{8} x-\frac{3}{8}=-\frac{3}{8}$$

Me tāpiri \frac{3}{8} ki ngā taha e rua o te whārite.

$$x=\frac{3}{4} x=0$$