Whakaoti i te (2x+1*3x+1)-x^2

$$(2x+1 \times 3x+1)- { x }^{ 2 }$$

Aromātai

$$1+5x-x^{2}$$

Ngā Upane Otinga

Whakareatia te 1 ki te 3, ka 3.

$$2x+3x+1-x^{2}$$

Pahekotia te 2x me 3x, ka 5x.

$$5x+1-x^{2}$$

Tauwehe

$$-\left(x-\frac{5-\sqrt{29}}{2}\right)\left(x-\frac{\sqrt{29}+5}{2}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 1 ki te 3, ka 3.

$$factor(2x+3x+1-x^{2})$$

Pahekotia te 2x me 3x, ka 5x.

$$factor(5x+1-x^{2})$$

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.

$$-x^{2}+5x+1=0$$

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.

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

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\left(-1\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-5±\sqrt{25+4}}{2\left(-1\right)}$$

Tāpiri 25 ki te 4.

$$x=\frac{-5±\sqrt{29}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-5±\sqrt{29}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-5±\sqrt{29}}{-2} ina he tāpiri te ±. Tāpiri -5 ki te \sqrt{29}.

$$x=\frac{\sqrt{29}-5}{-2}$$

Whakawehe -5+\sqrt{29} ki te -2.

$$x=\frac{5-\sqrt{29}}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±\sqrt{29}}{-2} ina he tango te ±. Tango \sqrt{29} mai i -5.

$$x=\frac{-\sqrt{29}-5}{-2}$$

Whakawehe -5-\sqrt{29} ki te -2.

$$x=\frac{\sqrt{29}+5}{2}$$

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{5-\sqrt{29}}{2} mō te x_{1} me te \frac{5+\sqrt{29}}{2} mō te x_{2}.

$$-x^{2}+5x+1=-\left(x-\frac{5-\sqrt{29}}{2}\right)\left(x-\frac{\sqrt{29}+5}{2}\right)$$