Whakaoti i te x^2-6x=2x^2+6x

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

Whakaoti mō x

$$x=-12$$

$$x=0$$

Ngā Upane Whakamahi Tauwehe

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

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

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

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

Tangohia te 6x mai i ngā taha e rua.

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

Pahekotia te -6x me -6x, ka -12x.

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

Tauwehea te x.

$$x\left(-x-12\right)=0$$

Hei kimi otinga whārite, me whakaoti te x=0 me te -x-12=0.

$$x=0 x=-12$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

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

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

Tangohia te 6x mai i ngā taha e rua.

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

Pahekotia te -6x me -6x, ka -12x.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -12 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te \left(-12\right)^{2}.

$$x=\frac{-\left(-12\right)±12}{2\left(-1\right)}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±12}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{12±12}{-2}$$

Nā, me whakaoti te whārite x=\frac{12±12}{-2} ina he tāpiri te ±. Tāpiri 12 ki te 12.

$$x=\frac{24}{-2}$$

Whakawehe 24 ki te -2.

$$x=-12$$

Nā, me whakaoti te whārite x=\frac{12±12}{-2} ina he tango te ±. Tango 12 mai i 12.

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

Whakawehe 0 ki te -2.

$$x=0$$

Kua oti te whārite te whakatau.

$$x=-12 x=0$$

Ngā Upane mō te Whakaoti i te Pūrua

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

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

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

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

Tangohia te 6x mai i ngā taha e rua.

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

Pahekotia te -6x me -6x, ka -12x.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-12x}{-1}=\frac{0}{-1}$$

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

$$x^{2}+\left(-\frac{12}{-1}\right)x=\frac{0}{-1}$$

Whakawehe -12 ki te -1.

$$x^{2}+12x=\frac{0}{-1}$$

Whakawehe 0 ki te -1.

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

Whakawehea te 12, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 6. Nā, tāpiria te pūrua o te 6 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+12x+6^{2}=6^{2}$$

Pūrua 6.

$$x^{2}+12x+36=36$$

Tauwehea x^{2}+12x+36. 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}.

$$\left(x+6\right)^{2}=36$$

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

$$\sqrt{\left(x+6\right)^{2}}=\sqrt{36}$$

Whakarūnātia.

$$x+6=6 x+6=-6$$

Me tango 6 mai i ngā taha e rua o te whārite.

$$x=0 x=-12$$