Whakaoti i te {l}{(4x^2+9x+2)}{+(-2x^2+2x-3)}

$$\left. \begin{array} { l } { ( 4 x ^ { 2 } + 9 x + 2 ) } \\ { + ( - 2 x ^ { 2 } + 2 x - 3 ) } \end{array} \right.$$

Aromātai

$$2x^{2}+11x-1$$

Ngā Upane Otinga

Pahekotia te 4x^{2} me -2x^{2}, ka 2x^{2}.

$$2x^{2}+9x+2+2x-3$$

Pahekotia te 9x me 2x, ka 11x.

$$2x^{2}+11x+2-3$$

Tangohia te 3 i te 2, ka -1.

$$2x^{2}+11x-1$$

Tauwehe

$$2\left(x-\frac{-\sqrt{129}-11}{4}\right)\left(x-\frac{\sqrt{129}-11}{4}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 4x^{2} me -2x^{2}, ka 2x^{2}.

$$factor(2x^{2}+9x+2+2x-3)$$

Pahekotia te 9x me 2x, ka 11x.

$$factor(2x^{2}+11x+2-3)$$

Tangohia te 3 i te 2, ka -1.

$$factor(2x^{2}+11x-1)$$

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.

$$2x^{2}+11x-1=0$$

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.

$$x=\frac{-11±\sqrt{11^{2}-4\times 2\left(-1\right)}}{2\times 2}$$

Pūrua 11.

$$x=\frac{-11±\sqrt{121-4\times 2\left(-1\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-11±\sqrt{121-8\left(-1\right)}}{2\times 2}$$

Whakareatia -8 ki te -1.

$$x=\frac{-11±\sqrt{121+8}}{2\times 2}$$

Tāpiri 121 ki te 8.

$$x=\frac{-11±\sqrt{129}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-11±\sqrt{129}}{4}$$

Nā, me whakaoti te whārite x=\frac{-11±\sqrt{129}}{4} ina he tāpiri te ±. Tāpiri -11 ki te \sqrt{129}.

$$x=\frac{\sqrt{129}-11}{4}$$

Nā, me whakaoti te whārite x=\frac{-11±\sqrt{129}}{4} ina he tango te ±. Tango \sqrt{129} mai i -11.

$$x=\frac{-\sqrt{129}-11}{4}$$

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{-11+\sqrt{129}}{4} mō te x_{1} me te \frac{-11-\sqrt{129}}{4} mō te x_{2}.

$$2x^{2}+11x-1=2\left(x-\frac{\sqrt{129}-11}{4}\right)\left(x-\frac{-\sqrt{129}-11}{4}\right)$$