Whakaoti i te x^2-12x-112

$${ x }^{ 2 } -12x-112$$

Tauwehe

$$\left(x-\left(6-2\sqrt{37}\right)\right)\left(x-\left(2\sqrt{37}+6\right)\right)$$

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.

$$x^{2}-12x-112=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-112\right)}}{2}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\left(-112\right)}}{2}$$

Whakareatia -4 ki te -112.

$$x=\frac{-\left(-12\right)±\sqrt{144+448}}{2}$$

Tāpiri 144 ki te 448.

$$x=\frac{-\left(-12\right)±\sqrt{592}}{2}$$

Tuhia te pūtakerua o te 592.

$$x=\frac{-\left(-12\right)±4\sqrt{37}}{2}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±4\sqrt{37}}{2}$$

Nā, me whakaoti te whārite x=\frac{12±4\sqrt{37}}{2} ina he tāpiri te ±. Tāpiri 12 ki te 4\sqrt{37}.

$$x=\frac{4\sqrt{37}+12}{2}$$

Whakawehe 12+4\sqrt{37} ki te 2.

$$x=2\sqrt{37}+6$$

Nā, me whakaoti te whārite x=\frac{12±4\sqrt{37}}{2} ina he tango te ±. Tango 4\sqrt{37} mai i 12.

$$x=\frac{12-4\sqrt{37}}{2}$$

Whakawehe 12-4\sqrt{37} ki te 2.

$$x=6-2\sqrt{37}$$

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 6+2\sqrt{37} mō te x_{1} me te 6-2\sqrt{37} mō te x_{2}.

$$x^{2}-12x-112=\left(x-\left(2\sqrt{37}+6\right)\right)\left(x-\left(6-2\sqrt{37}\right)\right)$$

Aromātai

$$x^{2}-12x-112$$