Whakaoti i te -x^2+5x+14>0

$$- x ^ { 2 } + 5 x + 14 > 0$$

Whakaoti mō x

$$x\in \left(-2,7\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Me whakarea te koreōrite ki te -1 kia tōrunga ai te tau whakarea o te pū tino teitei i -x^{2}+5x+14. I te mea he tōraro a -1, ka huri te ahunga koreōrite.

$$x^{2}-5x-14<0$$

Kia whakaotia te koreōrite, me tauwehe te taha mauī. 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.

$$x^{2}-5x-14=0$$

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te 1 mō te a, te -5 mō te b, me te -14 mō te c i te ture pūrua.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\left(-14\right)}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{5±9}{2}$$

Whakaotia te whārite x=\frac{5±9}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$x=7 x=-2$$

Tuhia anō te koreōrite mā te whakamahi i ngā otinga i whiwhi.

$$\left(x-7\right)\left(x+2\right)<0$$

Kia tōraro te otinga, me tauaro rawa ngā tohu o te x-7 me te x+2. Whakaarohia te tauira ina he tōrunga te x-7 he tōraro te x+2.

$$x-7>0 x+2<0$$

He teka tēnei mō tētahi x ahakoa.

$$x\in \emptyset$$

Whakaarohia te tauira ina he tōrunga te x+2 he tōraro te x-7.

$$x+2>0 x-7<0$$

Te otinga e whakaea i ngā koreōrite e rua ko x\in \left(-2,7\right).

$$x\in \left(-2,7\right)$$

Ko te otinga whakamutunga ko te whakakotahi i ngā otinga kua whiwhi.

$$x\in \left(-2,7\right)$$