Whakaoti i te 9x(x+9)=0

$$9 x ( x + 9 ) = 0$$

Whakaoti mō x

$$x=-9$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

Whakamahia te āhuatanga tohatoha hei whakarea te 9x ki te x+9.

$$9x^{2}+81x=0$$

Tauwehea te x.

$$x\left(9x+81\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 9x+81=0.

$$x=0 x=-9$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 9x ki te x+9.

$$9x^{2}+81x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, 81 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-81±\sqrt{81^{2}}}{2\times 9}$$

Tuhia te pūtakerua o te 81^{2}.

$$x=\frac{-81±81}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{-81±81}{18}$$

Nā, me whakaoti te whārite x=\frac{-81±81}{18} ina he tāpiri te ±. Tāpiri -81 ki te 81.

$$x=\frac{0}{18}$$

Whakawehe 0 ki te 18.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-81±81}{18} ina he tango te ±. Tango 81 mai i -81.

$$x=-\frac{162}{18}$$

Whakawehe -162 ki te 18.

$$x=-9$$

Kua oti te whārite te whakatau.

$$x=0 x=-9$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 9x ki te x+9.

$$9x^{2}+81x=0$$

Whakawehea ngā taha e rua ki te 9.

$$\frac{9x^{2}+81x}{9}=\frac{0}{9}$$

Mā te whakawehe ki te 9 ka wetekia te whakareanga ki te 9.

$$x^{2}+\frac{81}{9}x=\frac{0}{9}$$

Whakawehe 81 ki te 9.

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

Whakawehe 0 ki te 9.

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

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 tango \frac{9}{2} mai i ngā taha e rua o te whārite.

$$x=0 x=-9$$