Whakaoti i te x^2-400x+37500=0

$${ x }^{ 2 } -400x+37500=0$$

Whakaoti mō x

$$x=150$$

$$x=250$$

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.

$$x^{2}-400x+37500=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -400 mō b, me 37500 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-400\right)±\sqrt{\left(-400\right)^{2}-4\times 37500}}{2}$$

Pūrua -400.

$$x=\frac{-\left(-400\right)±\sqrt{160000-4\times 37500}}{2}$$

Whakareatia -4 ki te 37500.

$$x=\frac{-\left(-400\right)±\sqrt{160000-150000}}{2}$$

Tāpiri 160000 ki te -150000.

$$x=\frac{-\left(-400\right)±\sqrt{10000}}{2}$$

Tuhia te pūtakerua o te 10000.

$$x=\frac{-\left(-400\right)±100}{2}$$

Ko te tauaro o -400 ko 400.

$$x=\frac{400±100}{2}$$

Nā, me whakaoti te whārite x=\frac{400±100}{2} ina he tāpiri te ±. Tāpiri 400 ki te 100.

$$x=\frac{500}{2}$$

Whakawehe 500 ki te 2.

$$x=250$$

Nā, me whakaoti te whārite x=\frac{400±100}{2} ina he tango te ±. Tango 100 mai i 400.

$$x=\frac{300}{2}$$

Whakawehe 300 ki te 2.

$$x=150$$

Kua oti te whārite te whakatau.

$$x=250 x=150$$

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.

$$x^{2}-400x+37500=0$$

Me tango 37500 mai i ngā taha e rua o te whārite.

$$x^{2}-400x+37500-37500=-37500$$

Mā te tango i te 37500 i a ia ake anō ka toe ko te 0.

$$x^{2}-400x=-37500$$

Whakawehea te -400, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -200. Nā, tāpiria te pūrua o te -200 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-400x+\left(-200\right)^{2}=-37500+\left(-200\right)^{2}$$

Pūrua -200.

$$x^{2}-400x+40000=-37500+40000$$

Tāpiri -37500 ki te 40000.

$$x^{2}-400x+40000=2500$$

Tauwehea x^{2}-400x+40000. 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}.

$$\left(x-200\right)^{2}=2500$$

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

$$\sqrt{\left(x-200\right)^{2}}=\sqrt{2500}$$

Whakarūnātia.

$$x-200=50 x-200=-50$$

Me tāpiri 200 ki ngā taha e rua o te whārite.

$$x=250 x=150$$