Whakaoti i te x-98x^2/40000=0

$$x - \frac { 98 x ^ { 2 } } { 40000 } = 0$$

Whakaoti mō x

$$x = \frac{20000}{49} = 408\frac{8}{49} \approx 408.163265306$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakareatia ngā taha e rua o te whārite ki te 40000.

$$40000x-98x^{2}=0$$

Tauwehea te x.

$$x\left(40000-98x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 40000-98x=0.

$$x=0 x=\frac{20000}{49}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 40000.

$$40000x-98x^{2}=0$$

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.

$$-98x^{2}+40000x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -98 mō a, 40000 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-40000±\sqrt{40000^{2}}}{2\left(-98\right)}$$

Tuhia te pūtakerua o te 40000^{2}.

$$x=\frac{-40000±40000}{2\left(-98\right)}$$

Whakareatia 2 ki te -98.

$$x=\frac{-40000±40000}{-196}$$

Nā, me whakaoti te whārite x=\frac{-40000±40000}{-196} ina he tāpiri te ±. Tāpiri -40000 ki te 40000.

$$x=\frac{0}{-196}$$

Whakawehe 0 ki te -196.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-40000±40000}{-196} ina he tango te ±. Tango 40000 mai i -40000.

$$x=-\frac{80000}{-196}$$

Whakahekea te hautanga \frac{-80000}{-196} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{20000}{49}$$

Kua oti te whārite te whakatau.

$$x=0 x=\frac{20000}{49}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 40000.

$$40000x-98x^{2}=0$$

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.

$$-98x^{2}+40000x=0$$

Whakawehea ngā taha e rua ki te -98.

$$\frac{-98x^{2}+40000x}{-98}=\frac{0}{-98}$$

Mā te whakawehe ki te -98 ka wetekia te whakareanga ki te -98.

$$x^{2}+\frac{40000}{-98}x=\frac{0}{-98}$$

Whakahekea te hautanga \frac{40000}{-98} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{20000}{49}x=\frac{0}{-98}$$

Whakawehe 0 ki te -98.

$$x^{2}-\frac{20000}{49}x=0$$

Whakawehea te -\frac{20000}{49}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{10000}{49}. Nā, tāpiria te pūrua o te -\frac{10000}{49} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{20000}{49}x+\left(-\frac{10000}{49}\right)^{2}=\left(-\frac{10000}{49}\right)^{2}$$

Pūruatia -\frac{10000}{49} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{20000}{49}x+\frac{100000000}{2401}=\frac{100000000}{2401}$$

Tauwehea x^{2}-\frac{20000}{49}x+\frac{100000000}{2401}. 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}.

$$\left(x-\frac{10000}{49}\right)^{2}=\frac{100000000}{2401}$$

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

$$\sqrt{\left(x-\frac{10000}{49}\right)^{2}}=\sqrt{\frac{100000000}{2401}}$$

Whakarūnātia.

$$x-\frac{10000}{49}=\frac{10000}{49} x-\frac{10000}{49}=-\frac{10000}{49}$$

Me tāpiri \frac{10000}{49} ki ngā taha e rua o te whārite.

$$x=\frac{20000}{49} x=0$$