Whakaoti i te 4x-2=2x^2

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

Whakaoti mō x

$$x=1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

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

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

Whakawehea ngā taha e rua ki te 2.

$$2x-1-x^{2}=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-x^{2}+2x-1=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=-\left(-1\right)=1$$

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.

$$a=1 b=1$$

Tuhia anō te -x^{2}+2x-1 hei \left(-x^{2}+x\right)+\left(x-1\right).

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

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

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

Whakatauwehea atu te kīanga pātahi x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

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

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

$$x=1 x=1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

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.

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

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

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

Pūrua 4.

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

Whakareatia -4 ki te -2.

$$x=\frac{-4±\sqrt{16+8\left(-2\right)}}{2\left(-2\right)}$$

Whakareatia 8 ki te -2.

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

Tāpiri 16 ki te -16.

$$x=\frac{-4±\sqrt{0}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 0.

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

Whakareatia 2 ki te -2.

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

Whakawehe -4 ki te -4.

$$x=1$$

Ngā Upane mō te Whakaoti i te Pūrua

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

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

Me tāpiri te 2 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

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.

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

Whakawehea ngā taha e rua ki te -2.

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

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

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

Whakawehe 4 ki te -2.

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

Whakawehe 2 ki te -2.

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

Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

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

Tāpiri -1 ki te 1.

$$x^{2}-2x+1=0$$

Tauwehea x^{2}-2x+1. 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}.

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

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

$$\sqrt{\left(x-1\right)^{2}}=\sqrt{0}$$

Whakarūnātia.

$$x-1=0 x-1=0$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$x=1 x=1$$

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

$$x=1$$