Whakaoti i te 2xdiv3xdiv9=8(6-x)

$$2x \div 3x \div 9=8(6-x)$$

Whakaoti mō x

$$x=18\sqrt{11}-54\approx 5.699246226$$

$$x=-18\sqrt{11}-54\approx -113.699246226$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 9.

$$\frac{2x}{3}x=72\left(6-x\right)$$

Tuhia te \frac{2x}{3}x hei hautanga kotahi.

$$\frac{2xx}{3}=72\left(6-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 72 ki te 6-x.

$$\frac{2xx}{3}=432-72x$$

Whakareatia te x ki te x, ka x^{2}.

$$\frac{2x^{2}}{3}=432-72x$$

Tangohia te 432 mai i ngā taha e rua.

$$\frac{2x^{2}}{3}-432=-72x$$

Me tāpiri te 72x ki ngā taha e rua.

$$\frac{2x^{2}}{3}-432+72x=0$$

Whakareatia ngā taha e rua o te whārite ki te 3.

$$2x^{2}-1296+216x=0$$

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.

$$2x^{2}+216x-1296=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 216 mō b, me -1296 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-216±\sqrt{216^{2}-4\times 2\left(-1296\right)}}{2\times 2}$$

Pūrua 216.

$$x=\frac{-216±\sqrt{46656-4\times 2\left(-1296\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-216±\sqrt{46656-8\left(-1296\right)}}{2\times 2}$$

Whakareatia -8 ki te -1296.

$$x=\frac{-216±\sqrt{46656+10368}}{2\times 2}$$

Tāpiri 46656 ki te 10368.

$$x=\frac{-216±\sqrt{57024}}{2\times 2}$$

Tuhia te pūtakerua o te 57024.

$$x=\frac{-216±72\sqrt{11}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-216±72\sqrt{11}}{4}$$

Nā, me whakaoti te whārite x=\frac{-216±72\sqrt{11}}{4} ina he tāpiri te ±. Tāpiri -216 ki te 72\sqrt{11}.

$$x=\frac{72\sqrt{11}-216}{4}$$

Whakawehe -216+72\sqrt{11} ki te 4.

$$x=18\sqrt{11}-54$$

Nā, me whakaoti te whārite x=\frac{-216±72\sqrt{11}}{4} ina he tango te ±. Tango 72\sqrt{11} mai i -216.

$$x=\frac{-72\sqrt{11}-216}{4}$$

Whakawehe -216-72\sqrt{11} ki te 4.

$$x=-18\sqrt{11}-54$$

Kua oti te whārite te whakatau.

$$x=18\sqrt{11}-54 x=-18\sqrt{11}-54$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 9.

$$\frac{2x}{3}x=72\left(6-x\right)$$

Tuhia te \frac{2x}{3}x hei hautanga kotahi.

$$\frac{2xx}{3}=72\left(6-x\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 72 ki te 6-x.

$$\frac{2xx}{3}=432-72x$$

Whakareatia te x ki te x, ka x^{2}.

$$\frac{2x^{2}}{3}=432-72x$$

Me tāpiri te 72x ki ngā taha e rua.

$$\frac{2x^{2}}{3}+72x=432$$

Whakareatia ngā taha e rua o te whārite ki te 3.

$$2x^{2}+216x=1296$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}+216x}{2}=\frac{1296}{2}$$

Mā te whakawehe ki te 2 ka wetekia te whakareanga ki te 2.

$$x^{2}+\frac{216}{2}x=\frac{1296}{2}$$

Whakawehe 216 ki te 2.

$$x^{2}+108x=\frac{1296}{2}$$

Whakawehe 1296 ki te 2.

$$x^{2}+108x=648$$

Whakawehea te 108, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 54. Nā, tāpiria te pūrua o te 54 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+108x+54^{2}=648+54^{2}$$

Pūrua 54.

$$x^{2}+108x+2916=648+2916$$

Tāpiri 648 ki te 2916.

$$x^{2}+108x+2916=3564$$

Tauwehea x^{2}+108x+2916. 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}.

$$\left(x+54\right)^{2}=3564$$

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

$$\sqrt{\left(x+54\right)^{2}}=\sqrt{3564}$$

Whakarūnātia.

$$x+54=18\sqrt{11} x+54=-18\sqrt{11}$$

Me tango 54 mai i ngā taha e rua o te whārite.

$$x=18\sqrt{11}-54 x=-18\sqrt{11}-54$$