Whakaoti i te (6-x)2x=18

$$(6-x)2x=18$$

Whakaoti mō x

$$x=3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 6-x ki te 2.

$$\left(12-2x\right)x=18$$

Whakamahia te āhuatanga tohatoha hei whakarea te 12-2x ki te x.

$$12x-2x^{2}=18$$

Tangohia te 18 mai i ngā taha e rua.

$$12x-2x^{2}-18=0$$

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.

$$-2x^{2}+12x-18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 12 mō b, me -18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-2\right)\left(-18\right)}}{2\left(-2\right)}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\left(-2\right)\left(-18\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-12±\sqrt{144+8\left(-18\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -18.

$$x=\frac{-12±\sqrt{144-144}}{2\left(-2\right)}$$

Tāpiri 144 ki te -144.

$$x=\frac{-12±\sqrt{0}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 0.

$$x=-\frac{12}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=-\frac{12}{-4}$$

Whakawehe -12 ki te -4.

$$x=3$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 6-x ki te 2.

$$\left(12-2x\right)x=18$$

Whakamahia te āhuatanga tohatoha hei whakarea te 12-2x ki te x.

$$12x-2x^{2}=18$$

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.

$$-2x^{2}+12x=18$$

Whakawehea ngā taha e rua ki te -2.

$$\frac{-2x^{2}+12x}{-2}=\frac{18}{-2}$$

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

$$x^{2}+\frac{12}{-2}x=\frac{18}{-2}$$

Whakawehe 12 ki te -2.

$$x^{2}-6x=\frac{18}{-2}$$

Whakawehe 18 ki te -2.

$$x^{2}-6x=-9$$

Whakawehea te -6, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -3. Nā, tāpiria te pūrua o te -3 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-6x+\left(-3\right)^{2}=-9+\left(-3\right)^{2}$$

Pūrua -3.

$$x^{2}-6x+9=-9+9$$

Tāpiri -9 ki te 9.

$$x^{2}-6x+9=0$$

Tauwehea x^{2}-6x+9. 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}.

$$\left(x-3\right)^{2}=0$$

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

$$\sqrt{\left(x-3\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$x-3=0 x-3=0$$

Me tāpiri 3 ki ngā taha e rua o te whārite.

$$x=3 x=3$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=3$$