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

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

Whakaoti mō x

$$x=\frac{1}{2}=0.5$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

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

Tāpirihia te -2 ki te 2, ka 0.

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

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 2-x.

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

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te x me -2x, ka -x.

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

Me tāpiri te x^{2} ki ngā taha e rua.

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

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

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

Tauwehea te x.

$$x\left(2x-1\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te 2x-1=0.

$$x=0 x=\frac{1}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

Tāpirihia te -2 ki te 2, ka 0.

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

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 2-x.

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

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te x me -2x, ka -x.

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

Me tāpiri te x^{2} ki ngā taha e rua.

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

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

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

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

$$x=\frac{-\left(-1\right)±\sqrt{1}}{2\times 2}$$

Tuhia te pūtakerua o te 1.

$$x=\frac{-\left(-1\right)±1}{2\times 2}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±1}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{1±1}{4}$$

Nā, me whakaoti te whārite x=\frac{1±1}{4} ina he tāpiri te ±. Tāpiri 1 ki te 1.

$$x=\frac{2}{4}$$

Whakahekea te hautanga \frac{2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{1±1}{4} ina he tango te ±. Tango 1 mai i 1.

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

Whakawehe 0 ki te 4.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=\frac{1}{2} x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

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

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

Tāpirihia te -2 ki te 2, ka 0.

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

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te 2-x.

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

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te x me -2x, ka -x.

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

Me tāpiri te x^{2} ki ngā taha e rua.

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

Pahekotia te x^{2} me x^{2}, ka 2x^{2}.

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

Whakawehea ngā taha e rua ki te 2.

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

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

$$x^{2}-\frac{1}{2}x=\frac{0}{2}$$

Whakawehe 0 ki te 2.

$$x^{2}-\frac{1}{2}x=0$$

Whakawehea te -\frac{1}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1}{4}. Nā, tāpiria te pūrua o te -\frac{1}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{1}{2}x+\left(-\frac{1}{4}\right)^{2}=\left(-\frac{1}{4}\right)^{2}$$

Pūruatia -\frac{1}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{1}{2}x+\frac{1}{16}=\frac{1}{16}$$

Tauwehea x^{2}-\frac{1}{2}x+\frac{1}{16}. 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}.

$$\left(x-\frac{1}{4}\right)^{2}=\frac{1}{16}$$

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

$$\sqrt{\left(x-\frac{1}{4}\right)^{2}}=\sqrt{\frac{1}{16}}$$

Whakarūnātia.

$$x-\frac{1}{4}=\frac{1}{4} x-\frac{1}{4}=-\frac{1}{4}$$

Me tāpiri \frac{1}{4} ki ngā taha e rua o te whārite.

$$x=\frac{1}{2} x=0$$