Whakaoti i te x^2+2x+1-5*4

$${ x }^{ 2 } +2x+1-5 \times 4$$

Aromātai

$$x^{2}+2x-19$$

Ngā Upane Otinga

Whakareatia te 5 ki te 4, ka 20.

$$x^{2}+2x+1-20$$

Tangohia te 20 i te 1, ka -19.

$$x^{2}+2x-19$$

Tauwehe

$$\left(x-\left(-2\sqrt{5}-1\right)\right)\left(x-\left(2\sqrt{5}-1\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 5 ki te 4, ka 20.

$$factor(x^{2}+2x+1-20)$$

Tangohia te 20 i te 1, ka -19.

$$factor(x^{2}+2x-19)$$

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.

$$x^{2}+2x-19=0$$

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.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-19\right)}}{2}$$

Pūrua 2.

$$x=\frac{-2±\sqrt{4-4\left(-19\right)}}{2}$$

Whakareatia -4 ki te -19.

$$x=\frac{-2±\sqrt{4+76}}{2}$$

Tāpiri 4 ki te 76.

$$x=\frac{-2±\sqrt{80}}{2}$$

Tuhia te pūtakerua o te 80.

$$x=\frac{-2±4\sqrt{5}}{2}$$

Nā, me whakaoti te whārite x=\frac{-2±4\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri -2 ki te 4\sqrt{5}.

$$x=\frac{4\sqrt{5}-2}{2}$$

Whakawehe -2+4\sqrt{5} ki te 2.

$$x=2\sqrt{5}-1$$

Nā, me whakaoti te whārite x=\frac{-2±4\sqrt{5}}{2} ina he tango te ±. Tango 4\sqrt{5} mai i -2.

$$x=\frac{-4\sqrt{5}-2}{2}$$

Whakawehe -2-4\sqrt{5} ki te 2.

$$x=-2\sqrt{5}-1$$

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 -1+2\sqrt{5} mō te x_{1} me te -1-2\sqrt{5} mō te x_{2}.

$$x^{2}+2x-19=\left(x-\left(2\sqrt{5}-1\right)\right)\left(x-\left(-2\sqrt{5}-1\right)\right)$$