Whakaoti i te 4x^2+3x=6-2x

$$4 x ^ { 2 } + 3 x = 6 - 2 x$$

Whakaoti mō x

$$x=-2$$

$$x=\frac{3}{4}=0.75$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 6 mai i ngā taha e rua.

$$4x^{2}+3x-6=-2x$$

Me tāpiri te 2x ki ngā taha e rua.

$$4x^{2}+3x-6+2x=0$$

Pahekotia te 3x me 2x, ka 5x.

$$4x^{2}+5x-6=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 4x^{2}+ax+bx-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=4\left(-6\right)=-24$$

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. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -24.

$$-1,24 -2,12 -3,8 -4,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+24=23 -2+12=10 -3+8=5 -4+6=2$$

Ko te otinga te takirua ka hoatu i te tapeke 5.

$$a=-3 b=8$$

Tuhia anō te 4x^{2}+5x-6 hei \left(4x^{2}-3x\right)+\left(8x-6\right).

$$\left(4x^{2}-3x\right)+\left(8x-6\right)$$

Tauwehea te x i te tuatahi me te 2 i te rōpū tuarua.

$$x\left(4x-3\right)+2\left(4x-3\right)$$

Whakatauwehea atu te kīanga pātahi 4x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(4x-3\right)\left(x+2\right)$$

Hei kimi otinga whārite, me whakaoti te 4x-3=0 me te x+2=0.

$$x=\frac{3}{4} x=-2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 6 mai i ngā taha e rua.

$$4x^{2}+3x-6=-2x$$

Me tāpiri te 2x ki ngā taha e rua.

$$4x^{2}+3x-6+2x=0$$

Pahekotia te 3x me 2x, ka 5x.

$$4x^{2}+5x-6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 4 mō a, 5 mō b, me -6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-5±\sqrt{5^{2}-4\times 4\left(-6\right)}}{2\times 4}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\times 4\left(-6\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-5±\sqrt{25-16\left(-6\right)}}{2\times 4}$$

Whakareatia -16 ki te -6.

$$x=\frac{-5±\sqrt{25+96}}{2\times 4}$$

Tāpiri 25 ki te 96.

$$x=\frac{-5±\sqrt{121}}{2\times 4}$$

Tuhia te pūtakerua o te 121.

$$x=\frac{-5±11}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-5±11}{8}$$

Nā, me whakaoti te whārite x=\frac{-5±11}{8} ina he tāpiri te ±. Tāpiri -5 ki te 11.

$$x=\frac{6}{8}$$

Whakahekea te hautanga \frac{6}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{3}{4}$$

Nā, me whakaoti te whārite x=\frac{-5±11}{8} ina he tango te ±. Tango 11 mai i -5.

$$x=-\frac{16}{8}$$

Whakawehe -16 ki te 8.

$$x=-2$$

Kua oti te whārite te whakatau.

$$x=\frac{3}{4} x=-2$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 2x ki ngā taha e rua.

$$4x^{2}+3x+2x=6$$

Pahekotia te 3x me 2x, ka 5x.

$$4x^{2}+5x=6$$

Whakawehea ngā taha e rua ki te 4.

$$\frac{4x^{2}+5x}{4}=\frac{6}{4}$$

Mā te whakawehe ki te 4 ka wetekia te whakareanga ki te 4.

$$x^{2}+\frac{5}{4}x=\frac{6}{4}$$

Whakahekea te hautanga \frac{6}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}+\frac{5}{4}x=\frac{3}{2}$$

Whakawehea te \frac{5}{4}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{5}{8}. Nā, tāpiria te pūrua o te \frac{5}{8} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{5}{4}x+\left(\frac{5}{8}\right)^{2}=\frac{3}{2}+\left(\frac{5}{8}\right)^{2}$$

Pūruatia \frac{5}{8} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{5}{4}x+\frac{25}{64}=\frac{3}{2}+\frac{25}{64}$$

Tāpiri \frac{3}{2} ki te \frac{25}{64} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}+\frac{5}{4}x+\frac{25}{64}=\frac{121}{64}$$

Tauwehea x^{2}+\frac{5}{4}x+\frac{25}{64}. 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}.

$$\left(x+\frac{5}{8}\right)^{2}=\frac{121}{64}$$

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

$$\sqrt{\left(x+\frac{5}{8}\right)^{2}}=\sqrt{\frac{121}{64}}$$

Whakarūnātia.

$$x+\frac{5}{8}=\frac{11}{8} x+\frac{5}{8}=-\frac{11}{8}$$

Me tango \frac{5}{8} mai i ngā taha e rua o te whārite.

$$x=\frac{3}{4} x=-2$$