Whakaoti i te (x+2)(x-3)=(3x-2)(x+3)

$$( x + 2 ) ( x - 3 ) = ( 3 x - 2 ) ( x + 3 )$$

Whakaoti mō x

$$x=-4$$

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x-3 ka whakakotahi i ngā kupu rite.

$$x^{2}-x-6=\left(3x-2\right)\left(x+3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-2 ki te x+3 ka whakakotahi i ngā kupu rite.

$$x^{2}-x-6=3x^{2}+7x-6$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$x^{2}-x-6-3x^{2}=7x-6$$

Pahekotia te x^{2} me -3x^{2}, ka -2x^{2}.

$$-2x^{2}-x-6=7x-6$$

Tangohia te 7x mai i ngā taha e rua.

$$-2x^{2}-x-6-7x=-6$$

Pahekotia te -x me -7x, ka -8x.

$$-2x^{2}-8x-6=-6$$

Me tāpiri te 6 ki ngā taha e rua.

$$-2x^{2}-8x-6+6=0$$

Tāpirihia te -6 ki te 6, ka 0.

$$-2x^{2}-8x=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, -8 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Tuhia te pūtakerua o te \left(-8\right)^{2}.

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

Ko te tauaro o -8 ko 8.

$$x=\frac{8±8}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{8±8}{-4}$$

Nā, me whakaoti te whārite x=\frac{8±8}{-4} ina he tāpiri te ±. Tāpiri 8 ki te 8.

$$x=\frac{16}{-4}$$

Whakawehe 16 ki te -4.

$$x=-4$$

Nā, me whakaoti te whārite x=\frac{8±8}{-4} ina he tango te ±. Tango 8 mai i 8.

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

Whakawehe 0 ki te -4.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-4 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te x+2 ki te x-3 ka whakakotahi i ngā kupu rite.

$$x^{2}-x-6=\left(3x-2\right)\left(x+3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-2 ki te x+3 ka whakakotahi i ngā kupu rite.

$$x^{2}-x-6=3x^{2}+7x-6$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$x^{2}-x-6-3x^{2}=7x-6$$

Pahekotia te x^{2} me -3x^{2}, ka -2x^{2}.

$$-2x^{2}-x-6=7x-6$$

Tangohia te 7x mai i ngā taha e rua.

$$-2x^{2}-x-6-7x=-6$$

Pahekotia te -x me -7x, ka -8x.

$$-2x^{2}-8x-6=-6$$

Me tāpiri te 6 ki ngā taha e rua.

$$-2x^{2}-8x=-6+6$$

Tāpirihia te -6 ki te 6, ka 0.

$$-2x^{2}-8x=0$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}-8x}{-2}=\frac{0}{-2}$$

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

$$x^{2}+\left(-\frac{8}{-2}\right)x=\frac{0}{-2}$$

Whakawehe -8 ki te -2.

$$x^{2}+4x=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$x^{2}+4x=0$$

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

$$x^{2}+4x+2^{2}=2^{2}$$

Pūrua 2.

$$x^{2}+4x+4=4$$

Tauwehea x^{2}+4x+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}.

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

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

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

Whakarūnātia.

$$x+2=2 x+2=-2$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$x=0 x=-4$$