Whakaoti i te 46x=x^2

$$46 x = x ^ { 2 }$$

Whakaoti mō x

$$x=46$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

$$46x-x^{2}=0$$

Tauwehea te x.

$$x\left(46-x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 46-x=0.

$$x=0 x=46$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$46x-x^{2}=0$$

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.

$$-x^{2}+46x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 46 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-46±\sqrt{46^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 46^{2}.

$$x=\frac{-46±46}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-46±46}{-2}$$

Nā, me whakaoti te whārite x=\frac{-46±46}{-2} ina he tāpiri te ±. Tāpiri -46 ki te 46.

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

Whakawehe 0 ki te -2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-46±46}{-2} ina he tango te ±. Tango 46 mai i -46.

$$x=-\frac{92}{-2}$$

Whakawehe -92 ki te -2.

$$x=46$$

Kua oti te whārite te whakatau.

$$x=0 x=46$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$46x-x^{2}=0$$

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.

$$-x^{2}+46x=0$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+46x}{-1}=\frac{0}{-1}$$

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

$$x^{2}+\frac{46}{-1}x=\frac{0}{-1}$$

Whakawehe 46 ki te -1.

$$x^{2}-46x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x^{2}-46x=0$$

Whakawehea te -46, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -23. Nā, tāpiria te pūrua o te -23 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-46x+\left(-23\right)^{2}=\left(-23\right)^{2}$$

Pūrua -23.

$$x^{2}-46x+529=529$$

Tauwehea x^{2}-46x+529. 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}.

$$\left(x-23\right)^{2}=529$$

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

$$\sqrt{\left(x-23\right)^{2}}=\sqrt{529}$$

Whakarūnātia.

$$x-23=23 x-23=-23$$

Me tāpiri 23 ki ngā taha e rua o te whārite.

$$x=46 x=0$$