Whakaoti i te 5x^2-6x=0

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

Whakaoti mō x

$$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(5x-6\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 5x-6=0.

$$x=0 x=\frac{6}{5}$$

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.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -6 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}}}{2\times 5}$$

Tuhia te pūtakerua o te \left(-6\right)^{2}.

$$x=\frac{-\left(-6\right)±6}{2\times 5}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±6}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{6±6}{10}$$

Nā, me whakaoti te whārite x=\frac{6±6}{10} ina he tāpiri te ±. Tāpiri 6 ki te 6.

$$x=\frac{12}{10}$$

Whakahekea te hautanga \frac{12}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{6}{5}$$

Nā, me whakaoti te whārite x=\frac{6±6}{10} ina he tango te ±. Tango 6 mai i 6.

$$x=\frac{0}{10}$$

Whakawehe 0 ki te 10.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{6}{5} x=0$$

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.

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

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}-6x}{5}=\frac{0}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$x^{2}-\frac{6}{5}x=\frac{0}{5}$$

Whakawehe 0 ki te 5.

$$x^{2}-\frac{6}{5}x=0$$

Whakawehea te -\frac{6}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{5}. Nā, tāpiria te pūrua o te -\frac{3}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{6}{5}x+\left(-\frac{3}{5}\right)^{2}=\left(-\frac{3}{5}\right)^{2}$$

Pūruatia -\frac{3}{5} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{6}{5}x+\frac{9}{25}=\frac{9}{25}$$

Tauwehea x^{2}-\frac{6}{5}x+\frac{9}{25}. 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}.

$$\left(x-\frac{3}{5}\right)^{2}=\frac{9}{25}$$

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

$$\sqrt{\left(x-\frac{3}{5}\right)^{2}}=\sqrt{\frac{9}{25}}$$

Whakarūnātia.

$$x-\frac{3}{5}=\frac{3}{5} x-\frac{3}{5}=-\frac{3}{5}$$

Me tāpiri \frac{3}{5} ki ngā taha e rua o te whārite.

$$x=\frac{6}{5} x=0$$