Whakaoti i te 3x^2-56=-2x

$$3 x ^ { 2 } - 56 = - 2 x$$

Whakaoti mō x

$$x = -\frac{14}{3} = -4\frac{2}{3} \approx -4.666666667$$

$$x=4$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Me tāpiri te 2x ki ngā taha e rua.

$$3x^{2}-56+2x=0$$

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

$$3x^{2}+2x-56=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei 3x^{2}+ax+bx-56. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=3\left(-56\right)=-168$$

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 -168.

$$-1,168 -2,84 -3,56 -4,42 -6,28 -7,24 -8,21 -12,14$$

Tātaihia te tapeke mō ia takirua.

$$-1+168=167 -2+84=82 -3+56=53 -4+42=38 -6+28=22 -7+24=17 -8+21=13 -12+14=2$$

Ko te otinga te takirua ka hoatu i te tapeke 2.

$$a=-12 b=14$$

Tuhia anō te 3x^{2}+2x-56 hei \left(3x^{2}-12x\right)+\left(14x-56\right).

$$\left(3x^{2}-12x\right)+\left(14x-56\right)$$

Tauwehea te 3x i te tuatahi me te 14 i te rōpū tuarua.

$$3x\left(x-4\right)+14\left(x-4\right)$$

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

$$\left(x-4\right)\left(3x+14\right)$$

Hei kimi otinga whārite, me whakaoti te x-4=0 me te 3x+14=0.

$$x=4 x=-\frac{14}{3}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me tāpiri te 2x ki ngā taha e rua.

$$3x^{2}-56+2x=0$$

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.

$$3x^{2}+2x-56=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 2 mō b, me -56 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\times 3\left(-56\right)}}{2\times 3}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\times 3\left(-56\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-2±\sqrt{4-12\left(-56\right)}}{2\times 3}$$

Whakareatia -12 ki te -56.

$$x=\frac{-2±\sqrt{4+672}}{2\times 3}$$

Tāpiri 4 ki te 672.

$$x=\frac{-2±\sqrt{676}}{2\times 3}$$

Tuhia te pūtakerua o te 676.

$$x=\frac{-2±26}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-2±26}{6}$$

Nā, me whakaoti te whārite x=\frac{-2±26}{6} ina he tāpiri te ±. Tāpiri -2 ki te 26.

$$x=\frac{24}{6}$$

Whakawehe 24 ki te 6.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{-2±26}{6} ina he tango te ±. Tango 26 mai i -2.

$$x=-\frac{28}{6}$$

Whakahekea te hautanga \frac{-28}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=-\frac{14}{3}$$

Kua oti te whārite te whakatau.

$$x=4 x=-\frac{14}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Me tāpiri te 2x ki ngā taha e rua.

$$3x^{2}-56+2x=0$$

Me tāpiri te 56 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$3x^{2}+2x=56$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3x^{2}+2x}{3}=\frac{56}{3}$$

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

$$x^{2}+\frac{2}{3}x=\frac{56}{3}$$

Whakawehea te \frac{2}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{3}. Nā, tāpiria te pūrua o te \frac{1}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{2}{3}x+\left(\frac{1}{3}\right)^{2}=\frac{56}{3}+\left(\frac{1}{3}\right)^{2}$$

Pūruatia \frac{1}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{2}{3}x+\frac{1}{9}=\frac{56}{3}+\frac{1}{9}$$

Tāpiri \frac{56}{3} ki te \frac{1}{9} 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.

$$x^{2}+\frac{2}{3}x+\frac{1}{9}=\frac{169}{9}$$

Tauwehea x^{2}+\frac{2}{3}x+\frac{1}{9}. 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}.

$$\left(x+\frac{1}{3}\right)^{2}=\frac{169}{9}$$

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

$$\sqrt{\left(x+\frac{1}{3}\right)^{2}}=\sqrt{\frac{169}{9}}$$

Whakarūnātia.

$$x+\frac{1}{3}=\frac{13}{3} x+\frac{1}{3}=-\frac{13}{3}$$

Me tango \frac{1}{3} mai i ngā taha e rua o te whārite.

$$x=4 x=-\frac{14}{3}$$