Whakaoti i te (x-1)(x-2)=30

$$(x-1)(x-2)=30$$

Whakaoti mō x

$$x=-4$$

$$x=7$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te x-2 ka whakakotahi i ngā kupu rite.

$$x^{2}-3x+2=30$$

Tangohia te 30 mai i ngā taha e rua.

$$x^{2}-3x+2-30=0$$

Tangohia te 30 i te 2, ka -28.

$$x^{2}-3x-28=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -3 mō b, me -28 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-28\right)}}{2}$$

Pūrua -3.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-28\right)}}{2}$$

Whakareatia -4 ki te -28.

$$x=\frac{-\left(-3\right)±\sqrt{9+112}}{2}$$

Tāpiri 9 ki te 112.

$$x=\frac{-\left(-3\right)±\sqrt{121}}{2}$$

Tuhia te pūtakerua o te 121.

$$x=\frac{-\left(-3\right)±11}{2}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±11}{2}$$

Nā, me whakaoti te whārite x=\frac{3±11}{2} ina he tāpiri te ±. Tāpiri 3 ki te 11.

$$x=\frac{14}{2}$$

Whakawehe 14 ki te 2.

$$x=7$$

Nā, me whakaoti te whārite x=\frac{3±11}{2} ina he tango te ±. Tango 11 mai i 3.

$$x=-\frac{8}{2}$$

Whakawehe -8 ki te 2.

$$x=-4$$

Kua oti te whārite te whakatau.

$$x=7 x=-4$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-1 ki te x-2 ka whakakotahi i ngā kupu rite.

$$x^{2}-3x+2=30$$

Tangohia te 2 mai i ngā taha e rua.

$$x^{2}-3x=30-2$$

Tangohia te 2 i te 30, ka 28.

$$x^{2}-3x=28$$

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.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=28+\left(-\frac{3}{2}\right)^{2}$$

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

$$x^{2}-3x+\frac{9}{4}=28+\frac{9}{4}$$

Tāpiri 28 ki te \frac{9}{4}.

$$x^{2}-3x+\frac{9}{4}=\frac{121}{4}$$

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}.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{121}{4}$$

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

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{121}{4}}$$

Whakarūnātia.

$$x-\frac{3}{2}=\frac{11}{2} x-\frac{3}{2}=-\frac{11}{2}$$

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

$$x=7 x=-4$$