Whakaoti i te (x-11)(2x+1)=(x-11)

$$(x-11)(2x+1)=(x-11)$$

Whakaoti mō x

$$x=11$$

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-11 ki te 2x+1 ka whakakotahi i ngā kupu rite.

$$2x^{2}-21x-11=x-11$$

Tangohia te x mai i ngā taha e rua.

$$2x^{2}-21x-11-x=-11$$

Pahekotia te -21x me -x, ka -22x.

$$2x^{2}-22x-11=-11$$

Me tāpiri te 11 ki ngā taha e rua.

$$2x^{2}-22x-11+11=0$$

Tāpirihia te -11 ki te 11, ka 0.

$$2x^{2}-22x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, -22 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-22\right)±\sqrt{\left(-22\right)^{2}}}{2\times 2}$$

Tuhia te pūtakerua o te \left(-22\right)^{2}.

$$x=\frac{-\left(-22\right)±22}{2\times 2}$$

Ko te tauaro o -22 ko 22.

$$x=\frac{22±22}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{22±22}{4}$$

Nā, me whakaoti te whārite x=\frac{22±22}{4} ina he tāpiri te ±. Tāpiri 22 ki te 22.

$$x=\frac{44}{4}$$

Whakawehe 44 ki te 4.

$$x=11$$

Nā, me whakaoti te whārite x=\frac{22±22}{4} ina he tango te ±. Tango 22 mai i 22.

$$x=\frac{0}{4}$$

Whakawehe 0 ki te 4.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=11 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x-11 ki te 2x+1 ka whakakotahi i ngā kupu rite.

$$2x^{2}-21x-11=x-11$$

Tangohia te x mai i ngā taha e rua.

$$2x^{2}-21x-11-x=-11$$

Pahekotia te -21x me -x, ka -22x.

$$2x^{2}-22x-11=-11$$

Me tāpiri te 11 ki ngā taha e rua.

$$2x^{2}-22x=-11+11$$

Tāpirihia te -11 ki te 11, ka 0.

$$2x^{2}-22x=0$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2x^{2}-22x}{2}=\frac{0}{2}$$

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

$$x^{2}+\left(-\frac{22}{2}\right)x=\frac{0}{2}$$

Whakawehe -22 ki te 2.

$$x^{2}-11x=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$x^{2}-11x=0$$

Whakawehea te -11, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{11}{2}. Nā, tāpiria te pūrua o te -\frac{11}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-11x+\left(-\frac{11}{2}\right)^{2}=\left(-\frac{11}{2}\right)^{2}$$

Pūruatia -\frac{11}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-11x+\frac{121}{4}=\frac{121}{4}$$

Tauwehea x^{2}-11x+\frac{121}{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}.

$$\left(x-\frac{11}{2}\right)^{2}=\frac{121}{4}$$

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

$$\sqrt{\left(x-\frac{11}{2}\right)^{2}}=\sqrt{\frac{121}{4}}$$

Whakarūnātia.

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

Me tāpiri \frac{11}{2} ki ngā taha e rua o te whārite.

$$x=11 x=0$$