Whakaoti i te (8x^2-2x+1)+(3x^2+5x-8)=

$$( 8 x ^ { 2 } - 2 x + 1 ) + ( 3 x ^ { 2 } + 5 x - 8 ) =$$

Aromātai

$$11x^{2}+3x-7$$

Ngā Upane Otinga

Pahekotia te 8x^{2} me 3x^{2}, ka 11x^{2}.

$$11x^{2}-2x+1+5x-8$$

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

$$11x^{2}+3x+1-8$$

Tangohia te 8 i te 1, ka -7.

$$11x^{2}+3x-7$$

Tauwehe

$$11\left(x-\frac{-\sqrt{317}-3}{22}\right)\left(x-\frac{\sqrt{317}-3}{22}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 8x^{2} me 3x^{2}, ka 11x^{2}.

$$factor(11x^{2}-2x+1+5x-8)$$

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

$$factor(11x^{2}+3x+1-8)$$

Tangohia te 8 i te 1, ka -7.

$$factor(11x^{2}+3x-7)$$

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.

$$11x^{2}+3x-7=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\times 11\left(-7\right)}}{2\times 11}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\times 11\left(-7\right)}}{2\times 11}$$

Whakareatia -4 ki te 11.

$$x=\frac{-3±\sqrt{9-44\left(-7\right)}}{2\times 11}$$

Whakareatia -44 ki te -7.

$$x=\frac{-3±\sqrt{9+308}}{2\times 11}$$

Tāpiri 9 ki te 308.

$$x=\frac{-3±\sqrt{317}}{2\times 11}$$

Whakareatia 2 ki te 11.

$$x=\frac{-3±\sqrt{317}}{22}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{317}}{22} ina he tāpiri te ±. Tāpiri -3 ki te \sqrt{317}.

$$x=\frac{\sqrt{317}-3}{22}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{317}}{22} ina he tango te ±. Tango \sqrt{317} mai i -3.

$$x=\frac{-\sqrt{317}-3}{22}$$

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{-3+\sqrt{317}}{22} mō te x_{1} me te \frac{-3-\sqrt{317}}{22} mō te x_{2}.

$$11x^{2}+3x-7=11\left(x-\frac{\sqrt{317}-3}{22}\right)\left(x-\frac{-\sqrt{317}-3}{22}\right)$$