Whakaoti i te 2x^2+4x+4=10

$$2 x ^ { 2 } + 4 x + 4 = 10$$

Whakaoti mō x

$$x=-3$$

$$x=1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 10 mai i ngā taha e rua.

$$2x^{2}+4x+4-10=0$$

Tangohia te 10 i te 4, ka -6.

$$2x^{2}+4x-6=0$$

Whakawehea ngā taha e rua ki te 2.

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

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.

$$a+b=2 ab=1\left(-3\right)=-3$$

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.

$$a=-1 b=3$$

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

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

Tauwehea te x i te tuatahi me te 3 i te rōpū tuarua.

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

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

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

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

$$x=1 x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$2x^{2}+4x+4=10$$

Me tango 10 mai i ngā taha e rua o te whārite.

$$2x^{2}+4x+4-10=10-10$$

Mā te tango i te 10 i a ia ake anō ka toe ko te 0.

$$2x^{2}+4x+4-10=0$$

Tango 10 mai i 4.

$$2x^{2}+4x-6=0$$

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

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

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\times 2\left(-6\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-4±\sqrt{16-8\left(-6\right)}}{2\times 2}$$

Whakareatia -8 ki te -6.

$$x=\frac{-4±\sqrt{16+48}}{2\times 2}$$

Tāpiri 16 ki te 48.

$$x=\frac{-4±\sqrt{64}}{2\times 2}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{-4±8}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-4±8}{4}$$

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

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

Whakawehe 4 ki te 4.

$$x=1$$

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

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

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

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.

$$2x^{2}+4x+4=10$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$2x^{2}+4x+4-4=10-4$$

Mā te tango i te 4 i a ia ake anō ka toe ko te 0.

$$2x^{2}+4x=10-4$$

Tango 4 mai i 10.

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

Whakawehea ngā taha e rua ki te 2.

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

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

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

Whakawehe 4 ki te 2.

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

Whakawehe 6 ki te 2.

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

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.

$$x^{2}+2x+1^{2}=3+1^{2}$$

Pūrua 1.

$$x^{2}+2x+1=3+1$$

Tāpiri 3 ki te 1.

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

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}.

$$\left(x+1\right)^{2}=4$$

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

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{4}$$

Whakarūnātia.

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

Me tango 1 mai i ngā taha e rua o te whārite.

$$x=1 x=-3$$