Whakaoti i te 60x=x^2

$$60 x = x ^ { 2 }$$

Whakaoti mō x

$$x=60$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Tangohia te x^{2} mai i ngā taha e rua.

$$60x-x^{2}=0$$

Tauwehea te x.

$$x\left(60-x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 60-x=0.

$$x=0 x=60$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

$$60x-x^{2}=0$$

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.

$$-x^{2}+60x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 60 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-60±\sqrt{60^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 60^{2}.

$$x=\frac{-60±60}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-60±60}{-2}$$

Nā, me whakaoti te whārite x=\frac{-60±60}{-2} ina he tāpiri te ±. Tāpiri -60 ki te 60.

$$x=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-60±60}{-2} ina he tango te ±. Tango 60 mai i -60.

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

Whakawehe -120 ki te -2.

$$x=60$$

Kua oti te whārite te whakatau.

$$x=0 x=60$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te x^{2} mai i ngā taha e rua.

$$60x-x^{2}=0$$

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.

$$-x^{2}+60x=0$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+60x}{-1}=\frac{0}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\frac{60}{-1}x=\frac{0}{-1}$$

Whakawehe 60 ki te -1.

$$x^{2}-60x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x^{2}-60x=0$$

Whakawehea te -60, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -30. Nā, tāpiria te pūrua o te -30 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-60x+\left(-30\right)^{2}=\left(-30\right)^{2}$$

Pūrua -30.

$$x^{2}-60x+900=900$$

Tauwehea x^{2}-60x+900. 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}.

$$\left(x-30\right)^{2}=900$$

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

$$\sqrt{\left(x-30\right)^{2}}=\sqrt{900}$$

Whakarūnātia.

$$x-30=30 x-30=-30$$

Me tāpiri 30 ki ngā taha e rua o te whārite.

$$x=60 x=0$$