Whakaoti i te (x+2)(x-1)=2-3x

$$( x + 2 ) ( x - 1 ) = 2 - 3 x$$

Whakaoti mō x

$$x=2\sqrt{2}-2\approx 0.828427125$$

$$x=-2\sqrt{2}-2\approx -4.828427125$$

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.

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

Tangohia te 2 mai i ngā taha e rua.

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

Tangohia te 2 i te -2, ka -4.

$$x^{2}+x-4=-3x$$

Me tāpiri te 3x ki ngā taha e rua.

$$x^{2}+x-4+3x=0$$

Pahekotia te x me 3x, ka 4x.

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

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

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

Pūrua 4.

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

Whakareatia -4 ki te -4.

$$x=\frac{-4±\sqrt{16+16}}{2}$$

Tāpiri 16 ki te 16.

$$x=\frac{-4±\sqrt{32}}{2}$$

Tuhia te pūtakerua o te 32.

$$x=\frac{-4±4\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{-4±4\sqrt{2}}{2} ina he tāpiri te ±. Tāpiri -4 ki te 4\sqrt{2}.

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

Whakawehe -4+4\sqrt{2} ki te 2.

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

Nā, me whakaoti te whārite x=\frac{-4±4\sqrt{2}}{2} ina he tango te ±. Tango 4\sqrt{2} mai i -4.

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

Whakawehe -4-4\sqrt{2} ki te 2.

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

Kua oti te whārite te whakatau.

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

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.

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

Me tāpiri te 3x ki ngā taha e rua.

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

Pahekotia te x me 3x, ka 4x.

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

Me tāpiri te 2 ki ngā taha e rua.

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

Tāpirihia te 2 ki te 2, ka 4.

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

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.

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

Pūrua 2.

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

Tāpiri 4 ki te 4.

$$x^{2}+4x+4=8$$

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}.

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

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

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{8}$$

Whakarūnātia.

$$x+2=2\sqrt{2} x+2=-2\sqrt{2}$$

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

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