Whakaoti i te 5x^2-30x=0

$$5 x ^ { 2 } - 30 x = 0$$

Whakaoti mō x

$$x=6$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(5x-30\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 5x-30=0.

$$x=0 x=6$$

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.

$$5x^{2}-30x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -30 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-30\right)±\sqrt{\left(-30\right)^{2}}}{2\times 5}$$

Tuhia te pūtakerua o te \left(-30\right)^{2}.

$$x=\frac{-\left(-30\right)±30}{2\times 5}$$

Ko te tauaro o -30 ko 30.

$$x=\frac{30±30}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{30±30}{10}$$

Nā, me whakaoti te whārite x=\frac{30±30}{10} ina he tāpiri te ±. Tāpiri 30 ki te 30.

$$x=\frac{60}{10}$$

Whakawehe 60 ki te 10.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{30±30}{10} ina he tango te ±. Tango 30 mai i 30.

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

Whakawehe 0 ki te 10.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=6 x=0$$

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.

$$5x^{2}-30x=0$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5x^{2}-30x}{5}=\frac{0}{5}$$

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

$$x^{2}+\left(-\frac{30}{5}\right)x=\frac{0}{5}$$

Whakawehe -30 ki te 5.

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

Whakawehe 0 ki te 5.

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

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

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

Pūrua -3.

$$x^{2}-6x+9=9$$

Tauwehea x^{2}-6x+9. 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}.

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

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

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

Whakarūnātia.

$$x-3=3 x-3=-3$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$x=6 x=0$$