Whakaoti i te 800x^2-60000x=0

$$800 x ^ { 2 } - 60000 x = 0$$

Whakaoti mō x

$$x=75$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tauwehea te x.

$$x\left(800x-60000\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 800x-60000=0.

$$x=0 x=75$$

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.

$$800x^{2}-60000x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 800 mō a, -60000 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-60000\right)±\sqrt{\left(-60000\right)^{2}}}{2\times 800}$$

Tuhia te pūtakerua o te \left(-60000\right)^{2}.

$$x=\frac{-\left(-60000\right)±60000}{2\times 800}$$

Ko te tauaro o -60000 ko 60000.

$$x=\frac{60000±60000}{2\times 800}$$

Whakareatia 2 ki te 800.

$$x=\frac{60000±60000}{1600}$$

Nā, me whakaoti te whārite x=\frac{60000±60000}{1600} ina he tāpiri te ±. Tāpiri 60000 ki te 60000.

$$x=\frac{120000}{1600}$$

Whakawehe 120000 ki te 1600.

$$x=75$$

Nā, me whakaoti te whārite x=\frac{60000±60000}{1600} ina he tango te ±. Tango 60000 mai i 60000.

$$x=\frac{0}{1600}$$

Whakawehe 0 ki te 1600.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=75 x=0$$

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.

$$800x^{2}-60000x=0$$

Whakawehea ngā taha e rua ki te 800.

$$\frac{800x^{2}-60000x}{800}=\frac{0}{800}$$

Mā te whakawehe ki te 800 ka wetekia te whakareanga ki te 800.

$$x^{2}+\left(-\frac{60000}{800}\right)x=\frac{0}{800}$$

Whakawehe -60000 ki te 800.

$$x^{2}-75x=\frac{0}{800}$$

Whakawehe 0 ki te 800.

$$x^{2}-75x=0$$

Whakawehea te -75, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{75}{2}. Nā, tāpiria te pūrua o te -\frac{75}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-75x+\left(-\frac{75}{2}\right)^{2}=\left(-\frac{75}{2}\right)^{2}$$

Pūruatia -\frac{75}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-75x+\frac{5625}{4}=\frac{5625}{4}$$

Tauwehea x^{2}-75x+\frac{5625}{4}. 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}.

$$\left(x-\frac{75}{2}\right)^{2}=\frac{5625}{4}$$

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

$$\sqrt{\left(x-\frac{75}{2}\right)^{2}}=\sqrt{\frac{5625}{4}}$$

Whakarūnātia.

$$x-\frac{75}{2}=\frac{75}{2} x-\frac{75}{2}=-\frac{75}{2}$$

Me tāpiri \frac{75}{2} ki ngā taha e rua o te whārite.

$$x=75 x=0$$