Whakaoti i te -6x^2+9x-6=-4x^2+x

$$- 6 x ^ { 2 } + 9 x - 6 = - 4 x ^ { 2 } + x$$

Whakaoti mō x

$$x=1$$

$$x=3$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$-6x^{2}+9x-6+4x^{2}=x$$

Pahekotia te -6x^{2} me 4x^{2}, ka -2x^{2}.

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

Tangohia te x mai i ngā taha e rua.

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

Pahekotia te 9x me -x, ka 8x.

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

Whakawehea ngā taha e rua ki te 2.

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

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=4 ab=-\left(-3\right)=3$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=3 b=1$$

Tuhia anō te -x^{2}+4x-3 hei \left(-x^{2}+3x\right)+\left(x-3\right).

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

Whakatauwehea atu -x i te -x^{2}+3x.

$$-x\left(x-3\right)+x-3$$

Whakatauwehea atu te kīanga pātahi x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-3\right)\left(-x+1\right)$$

Hei kimi otinga whārite, me whakaoti te x-3=0 me te -x+1=0.

$$x=3 x=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$-6x^{2}+9x-6+4x^{2}=x$$

Pahekotia te -6x^{2} me 4x^{2}, ka -2x^{2}.

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

Tangohia te x mai i ngā taha e rua.

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

Pahekotia te 9x me -x, ka 8x.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 8 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-2\right)\left(-6\right)}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-8±\sqrt{64+8\left(-6\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -6.

$$x=\frac{-8±\sqrt{64-48}}{2\left(-2\right)}$$

Tāpiri 64 ki te -48.

$$x=\frac{-8±\sqrt{16}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 16.

$$x=\frac{-8±4}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-8±4}{-4}$$

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

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

Whakawehe -4 ki te -4.

$$x=1$$

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

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

Whakawehe -12 ki te -4.

$$x=3$$

Kua oti te whārite te whakatau.

$$x=1 x=3$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 4x^{2} ki ngā taha e rua.

$$-6x^{2}+9x-6+4x^{2}=x$$

Pahekotia te -6x^{2} me 4x^{2}, ka -2x^{2}.

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

Tangohia te x mai i ngā taha e rua.

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

Pahekotia te 9x me -x, ka 8x.

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

Me tāpiri te 6 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

Whakawehea ngā taha e rua ki te -2.

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

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

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

Whakawehe 8 ki te -2.

$$x^{2}-4x=\frac{6}{-2}$$

Whakawehe 6 ki te -2.

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

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.

$$x^{2}-4x+\left(-2\right)^{2}=-3+\left(-2\right)^{2}$$

Pūrua -2.

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

Tāpiri -3 ki te 4.

$$x^{2}-4x+4=1$$

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}.

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

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

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

Whakarūnātia.

$$x-2=1 x-2=-1$$

Me tāpiri 2 ki ngā taha e rua o te whārite.

$$x=3 x=1$$