Whakaoti i te 12*8-12x-(8-x)x=77

$$12 \times 8 - 12 x - ( 8 - x ) x = 77$$

Whakaoti mō x

$$x=1$$

$$x=19$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 12 ki te 8, ka 96.

$$96-12x-\left(8-x\right)x=77$$

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

$$96-12x-\left(8x-x^{2}\right)=77$$

Hei kimi i te tauaro o 8x-x^{2}, kimihia te tauaro o ia taurangi.

$$96-12x-8x-\left(-x^{2}\right)=77$$

Ko te tauaro o -x^{2} ko x^{2}.

$$96-12x-8x+x^{2}=77$$

Pahekotia te -12x me -8x, ka -20x.

$$96-20x+x^{2}=77$$

Tangohia te 77 mai i ngā taha e rua.

$$96-20x+x^{2}-77=0$$

Tangohia te 77 i te 96, ka 19.

$$19-20x+x^{2}=0$$

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.

$$x^{2}-20x+19=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -20 mō b, me 19 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 19}}{2}$$

Pūrua -20.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\times 19}}{2}$$

Whakareatia -4 ki te 19.

$$x=\frac{-\left(-20\right)±\sqrt{400-76}}{2}$$

Tāpiri 400 ki te -76.

$$x=\frac{-\left(-20\right)±\sqrt{324}}{2}$$

Tuhia te pūtakerua o te 324.

$$x=\frac{-\left(-20\right)±18}{2}$$

Ko te tauaro o -20 ko 20.

$$x=\frac{20±18}{2}$$

Nā, me whakaoti te whārite x=\frac{20±18}{2} ina he tāpiri te ±. Tāpiri 20 ki te 18.

$$x=\frac{38}{2}$$

Whakawehe 38 ki te 2.

$$x=19$$

Nā, me whakaoti te whārite x=\frac{20±18}{2} ina he tango te ±. Tango 18 mai i 20.

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

Whakawehe 2 ki te 2.

$$x=1$$

Kua oti te whārite te whakatau.

$$x=19 x=1$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakareatia te 12 ki te 8, ka 96.

$$96-12x-\left(8-x\right)x=77$$

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

$$96-12x-\left(8x-x^{2}\right)=77$$

Hei kimi i te tauaro o 8x-x^{2}, kimihia te tauaro o ia taurangi.

$$96-12x-8x-\left(-x^{2}\right)=77$$

Ko te tauaro o -x^{2} ko x^{2}.

$$96-12x-8x+x^{2}=77$$

Pahekotia te -12x me -8x, ka -20x.

$$96-20x+x^{2}=77$$

Tangohia te 96 mai i ngā taha e rua.

$$-20x+x^{2}=77-96$$

Tangohia te 96 i te 77, ka -19.

$$-20x+x^{2}=-19$$

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.

$$x^{2}-20x=-19$$

Whakawehea te -20, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -10. Nā, tāpiria te pūrua o te -10 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-20x+\left(-10\right)^{2}=-19+\left(-10\right)^{2}$$

Pūrua -10.

$$x^{2}-20x+100=-19+100$$

Tāpiri -19 ki te 100.

$$x^{2}-20x+100=81$$

Tauwehea x^{2}-20x+100. 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}.

$$\left(x-10\right)^{2}=81$$

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

$$\sqrt{\left(x-10\right)^{2}}=\sqrt{81}$$

Whakarūnātia.

$$x-10=9 x-10=-9$$

Me tāpiri 10 ki ngā taha e rua o te whārite.

$$x=19 x=1$$