Whakaoti i te 9x=x^2=

$$9 x = x ^ { 2 } =$$

Whakaoti mō x

$$x=9$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

$$9x-x^{2}=0$$

Tauwehea te x.

$$x\left(9-x\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 9-x=0.

$$x=0 x=9$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$9x-x^{2}=0$$

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.

$$-x^{2}+9x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 9 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-9±\sqrt{9^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 9^{2}.

$$x=\frac{-9±9}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-9±9}{-2}$$

Nā, me whakaoti te whārite x=\frac{-9±9}{-2} ina he tāpiri te ±. Tāpiri -9 ki te 9.

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

Whakawehe 0 ki te -2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-9±9}{-2} ina he tango te ±. Tango 9 mai i -9.

$$x=-\frac{18}{-2}$$

Whakawehe -18 ki te -2.

$$x=9$$

Kua oti te whārite te whakatau.

$$x=0 x=9$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$9x-x^{2}=0$$

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.

$$-x^{2}+9x=0$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}+9x}{-1}=\frac{0}{-1}$$

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

$$x^{2}+\frac{9}{-1}x=\frac{0}{-1}$$

Whakawehe 9 ki te -1.

$$x^{2}-9x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

$$x^{2}-9x=0$$

Whakawehea te -9, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{9}{2}. Nā, tāpiria te pūrua o te -\frac{9}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-9x+\left(-\frac{9}{2}\right)^{2}=\left(-\frac{9}{2}\right)^{2}$$

Pūruatia -\frac{9}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-9x+\frac{81}{4}=\frac{81}{4}$$

Tauwehea x^{2}-9x+\frac{81}{4}. 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}.

$$\left(x-\frac{9}{2}\right)^{2}=\frac{81}{4}$$

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

$$\sqrt{\left(x-\frac{9}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Whakarūnātia.

$$x-\frac{9}{2}=\frac{9}{2} x-\frac{9}{2}=-\frac{9}{2}$$

Me tāpiri \frac{9}{2} ki ngā taha e rua o te whārite.

$$x=9 x=0$$