Whakaoti i te 28x^2+x-2

$$28 x ^ { 2 } + x - 2$$

Tauwehe

$$\left(4x-1\right)\left(7x+2\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 28x^{2}+ax+bx-2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=28\left(-2\right)=-56$$

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 -56.

$$-1,56 -2,28 -4,14 -7,8$$

Tātaihia te tapeke mō ia takirua.

$$-1+56=55 -2+28=26 -4+14=10 -7+8=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=-7 b=8$$

Tuhia anō te 28x^{2}+x-2 hei \left(28x^{2}-7x\right)+\left(8x-2\right).

$$\left(28x^{2}-7x\right)+\left(8x-2\right)$$

Tauwehea te 7x i te tuatahi me te 2 i te rōpū tuarua.

$$7x\left(4x-1\right)+2\left(4x-1\right)$$

Whakatauwehea atu te kīanga pātahi 4x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(4x-1\right)\left(7x+2\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$28x^{2}+x-2=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\times 28\left(-2\right)}}{2\times 28}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\times 28\left(-2\right)}}{2\times 28}$$

Whakareatia -4 ki te 28.

$$x=\frac{-1±\sqrt{1-112\left(-2\right)}}{2\times 28}$$

Whakareatia -112 ki te -2.

$$x=\frac{-1±\sqrt{1+224}}{2\times 28}$$

Tāpiri 1 ki te 224.

$$x=\frac{-1±\sqrt{225}}{2\times 28}$$

Tuhia te pūtakerua o te 225.

$$x=\frac{-1±15}{2\times 28}$$

Whakareatia 2 ki te 28.

$$x=\frac{-1±15}{56}$$

Nā, me whakaoti te whārite x=\frac{-1±15}{56} ina he tāpiri te ±. Tāpiri -1 ki te 15.

$$x=\frac{14}{56}$$

Whakahekea te hautanga \frac{14}{56} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$x=\frac{1}{4}$$

Nā, me whakaoti te whārite x=\frac{-1±15}{56} ina he tango te ±. Tango 15 mai i -1.

$$x=-\frac{16}{56}$$

Whakahekea te hautanga \frac{-16}{56} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$x=-\frac{2}{7}$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{1}{4} mō te x_{1} me te -\frac{2}{7} mō te x_{2}.

$$28x^{2}+x-2=28\left(x-\frac{1}{4}\right)\left(x-\left(-\frac{2}{7}\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$28x^{2}+x-2=28\left(x-\frac{1}{4}\right)\left(x+\frac{2}{7}\right)$$

Tango \frac{1}{4} mai i x mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$28x^{2}+x-2=28\times \frac{4x-1}{4}\left(x+\frac{2}{7}\right)$$

Tāpiri \frac{2}{7} ki te x 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.

$$28x^{2}+x-2=28\times \frac{4x-1}{4}\times \frac{7x+2}{7}$$

Whakareatia \frac{4x-1}{4} ki te \frac{7x+2}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$28x^{2}+x-2=28\times \frac{\left(4x-1\right)\left(7x+2\right)}{4\times 7}$$

Whakareatia 4 ki te 7.

$$28x^{2}+x-2=28\times \frac{\left(4x-1\right)\left(7x+2\right)}{28}$$

Whakakorea atu te tauwehe pūnoa nui rawa 28 i roto i te 28 me te 28.

$$28x^{2}+x-2=\left(4x-1\right)\left(7x+2\right)$$

Aromātai

$$28x^{2}+x-2$$