Whakaoti i te (x+6)-3*x+2=(x+6)*x

$$( x + 6 ) - 3 \cdot x + 2 = ( x + 6 ) \cdot x$$

Whakaoti mō x

$$x=2\sqrt{6}-4\approx 0.898979486$$

$$x=-2\sqrt{6}-4\approx -8.898979486$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$-2x+6+2=\left(x+6\right)x$$

Tāpirihia te 6 ki te 2, ka 8.

$$-2x+8=\left(x+6\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+6 ki te x.

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

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

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

Tangohia te 6x mai i ngā taha e rua.

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

Pahekotia te -2x me -6x, ka -8x.

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

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -8 mō b, me 8 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-8\right)±\sqrt{64+4\times 8}}{2\left(-1\right)}$$

Whakareatia 4 ki te 8.

$$x=\frac{-\left(-8\right)±\sqrt{64+32}}{2\left(-1\right)}$$

Tāpiri 64 ki te 32.

$$x=\frac{-\left(-8\right)±\sqrt{96}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 96.

$$x=\frac{-\left(-8\right)±4\sqrt{6}}{2\left(-1\right)}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±4\sqrt{6}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{8±4\sqrt{6}}{-2}$$

Nā, me whakaoti te whārite x=\frac{8±4\sqrt{6}}{-2} ina he tāpiri te ±. Tāpiri 8 ki te 4\sqrt{6}.

$$x=\frac{4\sqrt{6}+8}{-2}$$

Whakawehe 8+4\sqrt{6} ki te -2.

$$x=-2\sqrt{6}-4$$

Nā, me whakaoti te whārite x=\frac{8±4\sqrt{6}}{-2} ina he tango te ±. Tango 4\sqrt{6} mai i 8.

$$x=\frac{8-4\sqrt{6}}{-2}$$

Whakawehe 8-4\sqrt{6} ki te -2.

$$x=2\sqrt{6}-4$$

Kua oti te whārite te whakatau.

$$x=-2\sqrt{6}-4 x=2\sqrt{6}-4$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$-2x+6+2=\left(x+6\right)x$$

Tāpirihia te 6 ki te 2, ka 8.

$$-2x+8=\left(x+6\right)x$$

Whakamahia te āhuatanga tohatoha hei whakarea te x+6 ki te x.

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

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

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

Tangohia te 6x mai i ngā taha e rua.

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

Pahekotia te -2x me -6x, ka -8x.

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

Tangohia te 8 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-8x}{-1}=-\frac{8}{-1}$$

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

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

Whakawehe -8 ki te -1.

$$x^{2}+8x=-\frac{8}{-1}$$

Whakawehe -8 ki te -1.

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

Whakawehea te 8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 4. Nā, tāpiria te pūrua o te 4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Pūrua 4.

$$x^{2}+8x+16=8+16$$

Tāpiri 8 ki te 16.

$$x^{2}+8x+16=24$$

Tauwehea te x^{2}+8x+16. Ko te tikanga, ina ko x^{2}+bx+c he pūrua tika, ka taea te tauwehe i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+4\right)^{2}=24$$

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

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{24}$$

Whakarūnātia.

$$x+4=2\sqrt{6} x+4=-2\sqrt{6}$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$x=2\sqrt{6}-4 x=-2\sqrt{6}-4$$