Whakaoti i te 17x^2-2x=0

$$17 x ^ { 2 } - 2 x = 0$$

Whakaoti mō x

$$x=\frac{2}{17}\approx 0.117647059$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(17x-2\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 17x-2=0.

$$x=0 x=\frac{2}{17}$$

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.

$$17x^{2}-2x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 17 mō a, -2 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}}}{2\times 17}$$

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

$$x=\frac{-\left(-2\right)±2}{2\times 17}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±2}{2\times 17}$$

Whakareatia 2 ki te 17.

$$x=\frac{2±2}{34}$$

Nā, me whakaoti te whārite x=\frac{2±2}{34} ina he tāpiri te ±. Tāpiri 2 ki te 2.

$$x=\frac{4}{34}$$

Whakahekea te hautanga \frac{4}{34} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{2}{17}$$

Nā, me whakaoti te whārite x=\frac{2±2}{34} ina he tango te ±. Tango 2 mai i 2.

$$x=\frac{0}{34}$$

Whakawehe 0 ki te 34.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{2}{17} x=0$$

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.

$$17x^{2}-2x=0$$

Whakawehea ngā taha e rua ki te 17.

$$\frac{17x^{2}-2x}{17}=\frac{0}{17}$$

Mā te whakawehe ki te 17 ka wetekia te whakareanga ki te 17.

$$x^{2}-\frac{2}{17}x=\frac{0}{17}$$

Whakawehe 0 ki te 17.

$$x^{2}-\frac{2}{17}x=0$$

Whakawehea te -\frac{2}{17}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{17}. Nā, tāpiria te pūrua o te -\frac{1}{17} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{2}{17}x+\left(-\frac{1}{17}\right)^{2}=\left(-\frac{1}{17}\right)^{2}$$

Pūruatia -\frac{1}{17} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{2}{17}x+\frac{1}{289}=\frac{1}{289}$$

Tauwehea x^{2}-\frac{2}{17}x+\frac{1}{289}. 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}.

$$\left(x-\frac{1}{17}\right)^{2}=\frac{1}{289}$$

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

$$\sqrt{\left(x-\frac{1}{17}\right)^{2}}=\sqrt{\frac{1}{289}}$$

Whakarūnātia.

$$x-\frac{1}{17}=\frac{1}{17} x-\frac{1}{17}=-\frac{1}{17}$$

Me tāpiri \frac{1}{17} ki ngā taha e rua o te whārite.

$$x=\frac{2}{17} x=0$$