Whakaoti i te 3x^2-2=5x

$$3 x ^ { 2 } - 2 = 5 x$$

Whakaoti mō x

$$x=-\frac{1}{3}\approx -0.333333333$$

$$x=2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tangohia te 5x mai i ngā taha e rua.

$$3x^{2}-2-5x=0$$

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

$$3x^{2}-5x-2=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 3x^{2}+ax+bx-2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-5 ab=3\left(-2\right)=-6$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -6.

$$1,-6 2,-3$$

Tātaihia te tapeke mō ia takirua.

$$1-6=-5 2-3=-1$$

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

$$a=-6 b=1$$

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

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

Whakatauwehea atu 3x i te 3x^{2}-6x.

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

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

$$\left(x-2\right)\left(3x+1\right)$$

Hei kimi otinga whārite, me whakaoti te x-2=0 me te 3x+1=0.

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 5x mai i ngā taha e rua.

$$3x^{2}-2-5x=0$$

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.

$$3x^{2}-5x-2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -5 mō b, me -2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 3\left(-2\right)}}{2\times 3}$$

Pūrua -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 3\left(-2\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-5\right)±\sqrt{25-12\left(-2\right)}}{2\times 3}$$

Whakareatia -12 ki te -2.

$$x=\frac{-\left(-5\right)±\sqrt{25+24}}{2\times 3}$$

Tāpiri 25 ki te 24.

$$x=\frac{-\left(-5\right)±\sqrt{49}}{2\times 3}$$

Tuhia te pūtakerua o te 49.

$$x=\frac{-\left(-5\right)±7}{2\times 3}$$

Ko te tauaro o -5 ko 5.

$$x=\frac{5±7}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{5±7}{6}$$

Nā, me whakaoti te whārite x=\frac{5±7}{6} ina he tāpiri te ±. Tāpiri 5 ki te 7.

$$x=\frac{12}{6}$$

Whakawehe 12 ki te 6.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{5±7}{6} ina he tango te ±. Tango 7 mai i 5.

$$x=-\frac{2}{6}$$

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

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

Kua oti te whārite te whakatau.

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

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 5x mai i ngā taha e rua.

$$3x^{2}-2-5x=0$$

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

$$3x^{2}-5x=2$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}-5x}{3}=\frac{2}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$x^{2}-\frac{5}{3}x=\frac{2}{3}$$

Whakawehea te -\frac{5}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{6}. Nā, tāpiria te pūrua o te -\frac{5}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{5}{3}x+\left(-\frac{5}{6}\right)^{2}=\frac{2}{3}+\left(-\frac{5}{6}\right)^{2}$$

Pūruatia -\frac{5}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{5}{3}x+\frac{25}{36}=\frac{2}{3}+\frac{25}{36}$$

Tāpiri \frac{2}{3} ki te \frac{25}{36} 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.

$$x^{2}-\frac{5}{3}x+\frac{25}{36}=\frac{49}{36}$$

Tauwehea x^{2}-\frac{5}{3}x+\frac{25}{36}. 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}.

$$\left(x-\frac{5}{6}\right)^{2}=\frac{49}{36}$$

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

$$\sqrt{\left(x-\frac{5}{6}\right)^{2}}=\sqrt{\frac{49}{36}}$$

Whakarūnātia.

$$x-\frac{5}{6}=\frac{7}{6} x-\frac{5}{6}=-\frac{7}{6}$$

Me tāpiri \frac{5}{6} ki ngā taha e rua o te whārite.

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