Whakaoti i te x^2-120x+3600=0

$${ x }^{ 2 } -120x+3600=0$$

Whakaoti mō x

$$x=60$$

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.

$$x^{2}-120x+3600=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -120 mō b, me 3600 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-120\right)±\sqrt{\left(-120\right)^{2}-4\times 3600}}{2}$$

Pūrua -120.

$$x=\frac{-\left(-120\right)±\sqrt{14400-4\times 3600}}{2}$$

Whakareatia -4 ki te 3600.

$$x=\frac{-\left(-120\right)±\sqrt{14400-14400}}{2}$$

Tāpiri 14400 ki te -14400.

$$x=\frac{-\left(-120\right)±\sqrt{0}}{2}$$

Tuhia te pūtakerua o te 0.

$$x=-\frac{-120}{2}$$

Ko te tauaro o -120 ko 120.

$$x=\frac{120}{2}$$

Whakawehe 120 ki te 2.

$$x=60$$

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.

$$x^{2}-120x+3600=0$$

Tauwehea x^{2}-120x+3600. 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}.

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

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

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

Whakarūnātia.

$$x-60=0 x-60=0$$

Me tāpiri 60 ki ngā taha e rua o te whārite.

$$x=60 x=60$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=60$$