Whakaoti i te 2x^2-60x=0

$$2 { x }^{ 2 } -60x=0$$

Whakaoti mō x

$$x=30$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(2x-60\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 2x-60=0.

$$x=0 x=30$$

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.

$$2x^{2}-60x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -60 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-60\right)±\sqrt{\left(-60\right)^{2}}}{2\times 2}$$

Tuhia te pūtakerua o te \left(-60\right)^{2}.

$$x=\frac{-\left(-60\right)±60}{2\times 2}$$

Ko te tauaro o -60 ko 60.

$$x=\frac{60±60}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{60±60}{4}$$

Nā, me whakaoti te whārite x=\frac{60±60}{4} ina he tāpiri te ±. Tāpiri 60 ki te 60.

$$x=\frac{120}{4}$$

Whakawehe 120 ki te 4.

$$x=30$$

Nā, me whakaoti te whārite x=\frac{60±60}{4} ina he tango te ±. Tango 60 mai i 60.

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

Whakawehe 0 ki te 4.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=30 x=0$$

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.

$$2x^{2}-60x=0$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-60x}{2}=\frac{0}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\left(-\frac{60}{2}\right)x=\frac{0}{2}$$

Whakawehe -60 ki te 2.

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

Whakawehe 0 ki te 2.

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

Whakawehea te -30, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -15. Nā, tāpiria te pūrua o te -15 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-30x+\left(-15\right)^{2}=\left(-15\right)^{2}$$

Pūrua -15.

$$x^{2}-30x+225=225$$

Tauwehea x^{2}-30x+225. 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}.

$$\left(x-15\right)^{2}=225$$

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

$$\sqrt{\left(x-15\right)^{2}}=\sqrt{225}$$

Whakarūnātia.

$$x-15=15 x-15=-15$$

Me tāpiri 15 ki ngā taha e rua o te whārite.

$$x=30 x=0$$