Whakaoti i te 7x^2-8x=0

$$7 x ^ { 2 } - 8 x = 0$$

Whakaoti mō x

$$x = \frac{8}{7} = 1\frac{1}{7} \approx 1.142857143$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(7x-8\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 7x-8=0.

$$x=0 x=\frac{8}{7}$$

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.

$$7x^{2}-8x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 7 mō a, -8 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Tuhia te pūtakerua o te \left(-8\right)^{2}.

$$x=\frac{-\left(-8\right)±8}{2\times 7}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±8}{2\times 7}$$

Whakareatia 2 ki te 7.

$$x=\frac{8±8}{14}$$

Nā, me whakaoti te whārite x=\frac{8±8}{14} ina he tāpiri te ±. Tāpiri 8 ki te 8.

$$x=\frac{16}{14}$$

Whakahekea te hautanga \frac{16}{14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

Nā, me whakaoti te whārite x=\frac{8±8}{14} ina he tango te ±. Tango 8 mai i 8.

$$x=\frac{0}{14}$$

Whakawehe 0 ki te 14.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{8}{7} x=0$$

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.

$$7x^{2}-8x=0$$

Whakawehea ngā taha e rua ki te 7.

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

Mā te whakawehe ki te 7 ka wetekia te whakareanga ki te 7.

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

Whakawehe 0 ki te 7.

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

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

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

Pūruatia -\frac{4}{7} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{8}{7}x+\frac{16}{49}=\frac{16}{49}$$

Tauwehea te x^{2}-\frac{8}{7}x+\frac{16}{49}. 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}.

$$\left(x-\frac{4}{7}\right)^{2}=\frac{16}{49}$$

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

$$\sqrt{\left(x-\frac{4}{7}\right)^{2}}=\sqrt{\frac{16}{49}}$$

Whakarūnātia.

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

Me tāpiri \frac{4}{7} ki ngā taha e rua o te whārite.

$$x=\frac{8}{7} x=0$$