Whakaoti i te x^2-15000x+50000=0

$$x ^ { 2 } - 15000 x + 50000 = 0$$

Whakaoti mō x

$$x=200\sqrt{1405}+7500\approx 14996.665925597$$

$$x=7500-200\sqrt{1405}\approx 3.334074403$$

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.

$$x^{2}-15000x+50000=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -15000 mō b, me 50000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-15000\right)±\sqrt{\left(-15000\right)^{2}-4\times 50000}}{2}$$

Pūrua -15000.

$$x=\frac{-\left(-15000\right)±\sqrt{225000000-4\times 50000}}{2}$$

Whakareatia -4 ki te 50000.

$$x=\frac{-\left(-15000\right)±\sqrt{225000000-200000}}{2}$$

Tāpiri 225000000 ki te -200000.

$$x=\frac{-\left(-15000\right)±\sqrt{224800000}}{2}$$

Tuhia te pūtakerua o te 224800000.

$$x=\frac{-\left(-15000\right)±400\sqrt{1405}}{2}$$

Ko te tauaro o -15000 ko 15000.

$$x=\frac{15000±400\sqrt{1405}}{2}$$

Nā, me whakaoti te whārite x=\frac{15000±400\sqrt{1405}}{2} ina he tāpiri te ±. Tāpiri 15000 ki te 400\sqrt{1405}.

$$x=\frac{400\sqrt{1405}+15000}{2}$$

Whakawehe 15000+400\sqrt{1405} ki te 2.

$$x=200\sqrt{1405}+7500$$

Nā, me whakaoti te whārite x=\frac{15000±400\sqrt{1405}}{2} ina he tango te ±. Tango 400\sqrt{1405} mai i 15000.

$$x=\frac{15000-400\sqrt{1405}}{2}$$

Whakawehe 15000-400\sqrt{1405} ki te 2.

$$x=7500-200\sqrt{1405}$$

Kua oti te whārite te whakatau.

$$x=200\sqrt{1405}+7500 x=7500-200\sqrt{1405}$$

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.

$$x^{2}-15000x+50000=0$$

Me tango 50000 mai i ngā taha e rua o te whārite.

$$x^{2}-15000x+50000-50000=-50000$$

Mā te tango i te 50000 i a ia ake anō ka toe ko te 0.

$$x^{2}-15000x=-50000$$

Whakawehea te -15000, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -7500. Nā, tāpiria te pūrua o te -7500 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-15000x+\left(-7500\right)^{2}=-50000+\left(-7500\right)^{2}$$

Pūrua -7500.

$$x^{2}-15000x+56250000=-50000+56250000$$

Tāpiri -50000 ki te 56250000.

$$x^{2}-15000x+56250000=56200000$$

Tauwehea x^{2}-15000x+56250000. 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}.

$$\left(x-7500\right)^{2}=56200000$$

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

$$\sqrt{\left(x-7500\right)^{2}}=\sqrt{56200000}$$

Whakarūnātia.

$$x-7500=200\sqrt{1405} x-7500=-200\sqrt{1405}$$

Me tāpiri 7500 ki ngā taha e rua o te whārite.

$$x=200\sqrt{1405}+7500 x=7500-200\sqrt{1405}$$