Whakaoti i te 8x(x-9)=0

$$8 x ( x - 9 ) = 0$$

Whakaoti mō x

$$x=9$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te 8x ki te x-9.

$$8x^{2}-72x=0$$

Tauwehea te x.

$$x\left(8x-72\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 8x-72=0.

$$x=0 x=9$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 8x ki te x-9.

$$8x^{2}-72x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 8 mō a, -72 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}}}{2\times 8}$$

Tuhia te pūtakerua o te \left(-72\right)^{2}.

$$x=\frac{-\left(-72\right)±72}{2\times 8}$$

Ko te tauaro o -72 ko 72.

$$x=\frac{72±72}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{72±72}{16}$$

Nā, me whakaoti te whārite x=\frac{72±72}{16} ina he tāpiri te ±. Tāpiri 72 ki te 72.

$$x=\frac{144}{16}$$

Whakawehe 144 ki te 16.

$$x=9$$

Nā, me whakaoti te whārite x=\frac{72±72}{16} ina he tango te ±. Tango 72 mai i 72.

$$x=\frac{0}{16}$$

Whakawehe 0 ki te 16.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=9 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 8x ki te x-9.

$$8x^{2}-72x=0$$

Whakawehea ngā taha e rua ki te 8.

$$\frac{8x^{2}-72x}{8}=\frac{0}{8}$$

Mā te whakawehe ki te 8 ka wetekia te whakareanga ki te 8.

$$x^{2}+\left(-\frac{72}{8}\right)x=\frac{0}{8}$$

Whakawehe -72 ki te 8.

$$x^{2}-9x=\frac{0}{8}$$

Whakawehe 0 ki te 8.

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

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.

$$x=9 x=0$$