Whakaoti i te x^2+5x-750

$$x ^ { 2 } + 5 x - 750$$

Tauwehe

$$\left(x-25\right)\left(x+30\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-750. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=1\left(-750\right)=-750$$

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 -750.

$$-1,750 -2,375 -3,250 -5,150 -6,125 -10,75 -15,50 -25,30$$

Tātaihia te tapeke mō ia takirua.

$$-1+750=749 -2+375=373 -3+250=247 -5+150=145 -6+125=119 -10+75=65 -15+50=35 -25+30=5$$

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

$$a=-25 b=30$$

Tuhia anō te x^{2}+5x-750 hei \left(x^{2}-25x\right)+\left(30x-750\right).

$$\left(x^{2}-25x\right)+\left(30x-750\right)$$

Tauwehea te x i te tuatahi me te 30 i te rōpū tuarua.

$$x\left(x-25\right)+30\left(x-25\right)$$

Whakatauwehea atu te kīanga pātahi x-25 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-25\right)\left(x+30\right)$$

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.

$$x^{2}+5x-750=0$$

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.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-750\right)}}{2}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\left(-750\right)}}{2}$$

Whakareatia -4 ki te -750.

$$x=\frac{-5±\sqrt{25+3000}}{2}$$

Tāpiri 25 ki te 3000.

$$x=\frac{-5±\sqrt{3025}}{2}$$

Tuhia te pūtakerua o te 3025.

$$x=\frac{-5±55}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±55}{2} ina he tāpiri te ±. Tāpiri -5 ki te 55.

$$x=\frac{50}{2}$$

Whakawehe 50 ki te 2.

$$x=25$$

Nā, me whakaoti te whārite x=\frac{-5±55}{2} ina he tango te ±. Tango 55 mai i -5.

$$x=-\frac{60}{2}$$

Whakawehe -60 ki te 2.

$$x=-30$$

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 25 mō te x_{1} me te -30 mō te x_{2}.

$$x^{2}+5x-750=\left(x-25\right)\left(x-\left(-30\right)\right)$$

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

$$x^{2}+5x-750=\left(x-25\right)\left(x+30\right)$$

Aromātai

$$\left(x-25\right)\left(x+30\right)$$