Whakaoti i te 4xdiv8*9(x-1)=10

$$4x \div 8 \times 9(x-1)=10$$

Whakaoti mō x

$$x=\frac{\sqrt{89}}{6}+\frac{1}{2}\approx 2.072330189$$

$$x=-\frac{\sqrt{89}}{6}+\frac{1}{2}\approx -1.072330189$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 8.

$$4x\times 9\left(x-1\right)=80$$

Whakareatia te 4 ki te 9, ka 36.

$$36x\left(x-1\right)=80$$

Whakamahia te āhuatanga tohatoha hei whakarea te 36x ki te x-1.

$$36x^{2}-36x=80$$

Tangohia te 80 mai i ngā taha e rua.

$$36x^{2}-36x-80=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 36 mō a, -36 mō b, me -80 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 36\left(-80\right)}}{2\times 36}$$

Pūrua -36.

$$x=\frac{-\left(-36\right)±\sqrt{1296-4\times 36\left(-80\right)}}{2\times 36}$$

Whakareatia -4 ki te 36.

$$x=\frac{-\left(-36\right)±\sqrt{1296-144\left(-80\right)}}{2\times 36}$$

Whakareatia -144 ki te -80.

$$x=\frac{-\left(-36\right)±\sqrt{1296+11520}}{2\times 36}$$

Tāpiri 1296 ki te 11520.

$$x=\frac{-\left(-36\right)±\sqrt{12816}}{2\times 36}$$

Tuhia te pūtakerua o te 12816.

$$x=\frac{-\left(-36\right)±12\sqrt{89}}{2\times 36}$$

Ko te tauaro o -36 ko 36.

$$x=\frac{36±12\sqrt{89}}{2\times 36}$$

Whakareatia 2 ki te 36.

$$x=\frac{36±12\sqrt{89}}{72}$$

Nā, me whakaoti te whārite x=\frac{36±12\sqrt{89}}{72} ina he tāpiri te ±. Tāpiri 36 ki te 12\sqrt{89}.

$$x=\frac{12\sqrt{89}+36}{72}$$

Whakawehe 36+12\sqrt{89} ki te 72.

$$x=\frac{\sqrt{89}}{6}+\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{36±12\sqrt{89}}{72} ina he tango te ±. Tango 12\sqrt{89} mai i 36.

$$x=\frac{36-12\sqrt{89}}{72}$$

Whakawehe 36-12\sqrt{89} ki te 72.

$$x=-\frac{\sqrt{89}}{6}+\frac{1}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{89}}{6}+\frac{1}{2} x=-\frac{\sqrt{89}}{6}+\frac{1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia ngā taha e rua o te whārite ki te 8.

$$4x\times 9\left(x-1\right)=80$$

Whakareatia te 4 ki te 9, ka 36.

$$36x\left(x-1\right)=80$$

Whakamahia te āhuatanga tohatoha hei whakarea te 36x ki te x-1.

$$36x^{2}-36x=80$$

Whakawehea ngā taha e rua ki te 36.

$$\frac{36x^{2}-36x}{36}=\frac{80}{36}$$

Mā te whakawehe ki te 36 ka wetekia te whakareanga ki te 36.

$$x^{2}+\left(-\frac{36}{36}\right)x=\frac{80}{36}$$

Whakawehe -36 ki te 36.

$$x^{2}-x=\frac{80}{36}$$

Whakahekea te hautanga \frac{80}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x^{2}-x=\frac{20}{9}$$

Whakawehea te -1, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{2}. Nā, tāpiria te pūrua o te -\frac{1}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=\frac{20}{9}+\left(-\frac{1}{2}\right)^{2}$$

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-x+\frac{1}{4}=\frac{20}{9}+\frac{1}{4}$$

Tāpiri \frac{20}{9} ki te \frac{1}{4} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}-x+\frac{1}{4}=\frac{89}{36}$$

Tauwehea x^{2}-x+\frac{1}{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}.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{89}{36}$$

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

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{89}{36}}$$

Whakarūnātia.

$$x-\frac{1}{2}=\frac{\sqrt{89}}{6} x-\frac{1}{2}=-\frac{\sqrt{89}}{6}$$

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$x=\frac{\sqrt{89}}{6}+\frac{1}{2} x=-\frac{\sqrt{89}}{6}+\frac{1}{2}$$