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

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

Whakaoti mō x

$$x=-1$$

$$x=2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

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

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

Whakawehea ngā taha e rua ki te 2.

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

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

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

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

$$a+b=1 ab=-2=-2$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=2 b=-1$$

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

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

Tauwehea te -x i te tuatahi me te -1 i te rōpū tuarua.

$$-x\left(x-2\right)-\left(x-2\right)$$

Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-2\right)\left(-x-1\right)$$

Hei kimi otinga whārite, me whakaoti te x-2=0 me te -x-1=0.

$$x=2 x=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

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.

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

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

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

Pūrua 2.

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

Whakareatia -4 ki te -2.

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

Whakareatia 8 ki te 4.

$$x=\frac{-2±\sqrt{4+32}}{2\left(-2\right)}$$

Tāpiri 4 ki te 32.

$$x=\frac{-2±\sqrt{36}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 36.

$$x=\frac{-2±6}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-2±6}{-4}$$

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

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

Whakawehe 4 ki te -4.

$$x=-1$$

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

$$x=-\frac{8}{-4}$$

Whakawehe -8 ki te -4.

$$x=2$$

Kua oti te whārite te whakatau.

$$x=-1 x=2$$

Ngā Upane mō te Whakaoti i te Pūrua

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

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

Tangohia te 4 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

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.

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

Whakawehea ngā taha e rua ki te -2.

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

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

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

Whakawehe 2 ki te -2.

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

Whakawehe -4 ki te -2.

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

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

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

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

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

Tāpiri 2 ki te \frac{1}{4}.

$$x^{2}-x+\frac{1}{4}=\frac{9}{4}$$

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

$$\left(x-\frac{1}{2}\right)^{2}=\frac{9}{4}$$

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

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Whakarūnātia.

$$x-\frac{1}{2}=\frac{3}{2} x-\frac{1}{2}=-\frac{3}{2}$$

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$x=2 x=-1$$