Whakaoti i te 18v^2+33v-30

$$18 v ^ { 2 } + 33 v - 30$$

Tauwehe

$$3\left(3v-2\right)\left(2v+5\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(6v^{2}+11v-10\right)$$

Whakaarohia te 6v^{2}+11v-10. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 6v^{2}+av+bv-10. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=11 ab=6\left(-10\right)=-60$$

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 -60.

$$-1,60 -2,30 -3,20 -4,15 -5,12 -6,10$$

Tātaihia te tapeke mō ia takirua.

$$-1+60=59 -2+30=28 -3+20=17 -4+15=11 -5+12=7 -6+10=4$$

Ko te otinga te takirua ka hoatu i te tapeke 11.

$$a=-4 b=15$$

Tuhia anō te 6v^{2}+11v-10 hei \left(6v^{2}-4v\right)+\left(15v-10\right).

$$\left(6v^{2}-4v\right)+\left(15v-10\right)$$

Tauwehea te 2v i te tuatahi me te 5 i te rōpū tuarua.

$$2v\left(3v-2\right)+5\left(3v-2\right)$$

Whakatauwehea atu te kīanga pātahi 3v-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3v-2\right)\left(2v+5\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3\left(3v-2\right)\left(2v+5\right)$$

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.

$$18v^{2}+33v-30=0$$

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.

$$v=\frac{-33±\sqrt{33^{2}-4\times 18\left(-30\right)}}{2\times 18}$$

Pūrua 33.

$$v=\frac{-33±\sqrt{1089-4\times 18\left(-30\right)}}{2\times 18}$$

Whakareatia -4 ki te 18.

$$v=\frac{-33±\sqrt{1089-72\left(-30\right)}}{2\times 18}$$

Whakareatia -72 ki te -30.

$$v=\frac{-33±\sqrt{1089+2160}}{2\times 18}$$

Tāpiri 1089 ki te 2160.

$$v=\frac{-33±\sqrt{3249}}{2\times 18}$$

Tuhia te pūtakerua o te 3249.

$$v=\frac{-33±57}{2\times 18}$$

Whakareatia 2 ki te 18.

$$v=\frac{-33±57}{36}$$

Nā, me whakaoti te whārite v=\frac{-33±57}{36} ina he tāpiri te ±. Tāpiri -33 ki te 57.

$$v=\frac{24}{36}$$

Whakahekea te hautanga \frac{24}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

$$v=\frac{2}{3}$$

Nā, me whakaoti te whārite v=\frac{-33±57}{36} ina he tango te ±. Tango 57 mai i -33.

$$v=-\frac{90}{36}$$

Whakahekea te hautanga \frac{-90}{36} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 18.

$$v=-\frac{5}{2}$$

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{2}{3} mō te x_{1} me te -\frac{5}{2} mō te x_{2}.

$$18v^{2}+33v-30=18\left(v-\frac{2}{3}\right)\left(v-\left(-\frac{5}{2}\right)\right)$$

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

$$18v^{2}+33v-30=18\left(v-\frac{2}{3}\right)\left(v+\frac{5}{2}\right)$$

Tango \frac{2}{3} mai i v 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.

$$18v^{2}+33v-30=18\times \frac{3v-2}{3}\left(v+\frac{5}{2}\right)$$

Tāpiri \frac{5}{2} ki te v 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.

$$18v^{2}+33v-30=18\times \frac{3v-2}{3}\times \frac{2v+5}{2}$$

Whakareatia \frac{3v-2}{3} ki te \frac{2v+5}{2} 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.

$$18v^{2}+33v-30=18\times \frac{\left(3v-2\right)\left(2v+5\right)}{3\times 2}$$

Whakareatia 3 ki te 2.

$$18v^{2}+33v-30=18\times \frac{\left(3v-2\right)\left(2v+5\right)}{6}$$

Whakakorea atu te tauwehe pūnoa nui rawa 6 i roto i te 18 me te 6.

$$18v^{2}+33v-30=3\left(3v-2\right)\left(2v+5\right)$$

Aromātai

$$18v^{2}+33v-30$$