Whakaoti i te 44=x(x-3)/2

$$44= \frac{ x(x-3) }{ 2 }$$

Whakaoti mō x

$$x=-8$$

$$x=11$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea ngā taha e rua ki te 2.

$$44\times 2=x\left(x-3\right)$$

Whakareatia te 44 ki te 2, ka 88.

$$88=x\left(x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-3.

$$88=x^{2}-3x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}-3x=88$$

Tangohia te 88 mai i ngā taha e rua.

$$x^{2}-3x-88=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -3 mō b, me -88 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-88\right)}}{2}$$

Pūrua -3.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-88\right)}}{2}$$

Whakareatia -4 ki te -88.

$$x=\frac{-\left(-3\right)±\sqrt{9+352}}{2}$$

Tāpiri 9 ki te 352.

$$x=\frac{-\left(-3\right)±\sqrt{361}}{2}$$

Tuhia te pūtakerua o te 361.

$$x=\frac{-\left(-3\right)±19}{2}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±19}{2}$$

Nā, me whakaoti te whārite x=\frac{3±19}{2} ina he tāpiri te ±. Tāpiri 3 ki te 19.

$$x=\frac{22}{2}$$

Whakawehe 22 ki te 2.

$$x=11$$

Nā, me whakaoti te whārite x=\frac{3±19}{2} ina he tango te ±. Tango 19 mai i 3.

$$x=-\frac{16}{2}$$

Whakawehe -16 ki te 2.

$$x=-8$$

Kua oti te whārite te whakatau.

$$x=11 x=-8$$

Ngā Upane mō te Whakaoti i te Pūrua

Me whakarea ngā taha e rua ki te 2.

$$44\times 2=x\left(x-3\right)$$

Whakareatia te 44 ki te 2, ka 88.

$$88=x\left(x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x-3.

$$88=x^{2}-3x$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$x^{2}-3x=88$$

Whakawehea te -3, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{2}. Nā, tāpiria te pūrua o te -\frac{3}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=88+\left(-\frac{3}{2}\right)^{2}$$

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-3x+\frac{9}{4}=88+\frac{9}{4}$$

Tāpiri 88 ki te \frac{9}{4}.

$$x^{2}-3x+\frac{9}{4}=\frac{361}{4}$$

Tauwehea x^{2}-3x+\frac{9}{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}.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{361}{4}$$

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

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{361}{4}}$$

Whakarūnātia.

$$x-\frac{3}{2}=\frac{19}{2} x-\frac{3}{2}=-\frac{19}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$x=11 x=-8$$