Whakaoti i te 12x^2+5x-27=3x^2-13x

$$12 x ^ { 2 } + 5 x - 27 = 3 x ^ { 2 } - 13 x$$

Whakaoti mō x

$$x=-3$$

$$x=1$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 3x^{2} mai i ngā taha e rua.

$$12x^{2}+5x-27-3x^{2}=-13x$$

Pahekotia te 12x^{2} me -3x^{2}, ka 9x^{2}.

$$9x^{2}+5x-27=-13x$$

Me tāpiri te 13x ki ngā taha e rua.

$$9x^{2}+5x-27+13x=0$$

Pahekotia te 5x me 13x, ka 18x.

$$9x^{2}+18x-27=0$$

Whakawehea ngā taha e rua ki te 9.

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

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

Tangohia te 3x^{2} mai i ngā taha e rua.

$$12x^{2}+5x-27-3x^{2}=-13x$$

Pahekotia te 12x^{2} me -3x^{2}, ka 9x^{2}.

$$9x^{2}+5x-27=-13x$$

Me tāpiri te 13x ki ngā taha e rua.

$$9x^{2}+5x-27+13x=0$$

Pahekotia te 5x me 13x, ka 18x.

$$9x^{2}+18x-27=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, 18 mō b, me -27 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-18±\sqrt{18^{2}-4\times 9\left(-27\right)}}{2\times 9}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\times 9\left(-27\right)}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-18±\sqrt{324-36\left(-27\right)}}{2\times 9}$$

Whakareatia -36 ki te -27.

$$x=\frac{-18±\sqrt{324+972}}{2\times 9}$$

Tāpiri 324 ki te 972.

$$x=\frac{-18±\sqrt{1296}}{2\times 9}$$

Tuhia te pūtakerua o te 1296.

$$x=\frac{-18±36}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{-18±36}{18}$$

Nā, me whakaoti te whārite x=\frac{-18±36}{18} ina he tāpiri te ±. Tāpiri -18 ki te 36.

$$x=\frac{18}{18}$$

Whakawehe 18 ki te 18.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{-18±36}{18} ina he tango te ±. Tango 36 mai i -18.

$$x=-\frac{54}{18}$$

Whakawehe -54 ki te 18.

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=1 x=-3$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 3x^{2} mai i ngā taha e rua.

$$12x^{2}+5x-27-3x^{2}=-13x$$

Pahekotia te 12x^{2} me -3x^{2}, ka 9x^{2}.

$$9x^{2}+5x-27=-13x$$

Me tāpiri te 13x ki ngā taha e rua.

$$9x^{2}+5x-27+13x=0$$

Pahekotia te 5x me 13x, ka 18x.

$$9x^{2}+18x-27=0$$

Me tāpiri te 27 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$9x^{2}+18x=27$$

Whakawehea ngā taha e rua ki te 9.

$$\frac{9x^{2}+18x}{9}=\frac{27}{9}$$

Mā te whakawehe ki te 9 ka wetekia te whakareanga ki te 9.

$$x^{2}+\frac{18}{9}x=\frac{27}{9}$$

Whakawehe 18 ki te 9.

$$x^{2}+2x=\frac{27}{9}$$

Whakawehe 27 ki te 9.

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

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.

$$x=1 x=-3$$