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

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

Whakaoti mō x

$$x=-2$$

$$x=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

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

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

Tangohia te 2x^{2} mai i ngā taha e rua.

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

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

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

Tangohia te 3x mai i ngā taha e rua.

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

Pahekotia te 2x me -3x, ka -x.

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

Me tāpiri te 2 ki ngā taha e rua.

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

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

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

Whakareatia -4 ki te -1.

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

Whakareatia 4 ki te 2.

$$x=\frac{-\left(-1\right)±\sqrt{1+8}}{2\left(-1\right)}$$

Tāpiri 1 ki te 8.

$$x=\frac{-\left(-1\right)±\sqrt{9}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 9.

$$x=\frac{-\left(-1\right)±3}{2\left(-1\right)}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±3}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{1±3}{-2}$$

Nā, me whakaoti te whārite x=\frac{1±3}{-2} ina he tāpiri te ±. Tāpiri 1 ki te 3.

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

Whakawehe 4 ki te -2.

$$x=-2$$

Nā, me whakaoti te whārite x=\frac{1±3}{-2} ina he tango te ±. Tango 3 mai i 1.

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

Whakawehe -2 ki te -2.

$$x=1$$

Kua oti te whārite te whakatau.

$$x=-2 x=1$$

Ngā Upane mō te Whakaoti i te Pūrua

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

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

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

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

Tangohia te 2x^{2} mai i ngā taha e rua.

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

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

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

Tangohia te 3x mai i ngā taha e rua.

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

Pahekotia te 2x me -3x, ka -x.

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

Whakawehea ngā taha e rua ki te -1.

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

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

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

Whakawehe -1 ki te -1.

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

Whakawehe -2 ki te -1.

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

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

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

Pūruatia \frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+x+\frac{1}{4}=2+\frac{1}{4}$$

Tāpiri 2 ki te \frac{1}{4}.

$$x^{2}+x+\frac{1}{4}=\frac{9}{4}$$

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

$$\left(x+\frac{1}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(x+\frac{1}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

$$x+\frac{1}{2}=\frac{3}{2} x+\frac{1}{2}=-\frac{3}{2}$$

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

$$x=1 x=-2$$