Whakaoti i te 12x^2+8x-3-7x^2+4x+5

$$12 x ^ { 2 } + 8 x - 3 - 7 x ^ { 2 } + 4 x + 5$$

Aromātai

$$5x^{2}+12x+2$$

Ngā Upane Otinga

Pahekotia te 12x^{2} me -7x^{2}, ka 5x^{2}.

$$5x^{2}+8x-3+4x+5$$

Pahekotia te 8x me 4x, ka 12x.

$$5x^{2}+12x-3+5$$

Tāpirihia te -3 ki te 5, ka 2.

$$5x^{2}+12x+2$$

Tauwehe

$$5\left(x-\frac{-\sqrt{26}-6}{5}\right)\left(x-\frac{\sqrt{26}-6}{5}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 12x^{2} me -7x^{2}, ka 5x^{2}.

$$factor(5x^{2}+8x-3+4x+5)$$

Pahekotia te 8x me 4x, ka 12x.

$$factor(5x^{2}+12x-3+5)$$

Tāpirihia te -3 ki te 5, ka 2.

$$factor(5x^{2}+12x+2)$$

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.

$$5x^{2}+12x+2=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 5\times 2}}{2\times 5}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 5\times 2}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-12±\sqrt{144-20\times 2}}{2\times 5}$$

Whakareatia -20 ki te 2.

$$x=\frac{-12±\sqrt{144-40}}{2\times 5}$$

Tāpiri 144 ki te -40.

$$x=\frac{-12±\sqrt{104}}{2\times 5}$$

Tuhia te pūtakerua o te 104.

$$x=\frac{-12±2\sqrt{26}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{-12±2\sqrt{26}}{10}$$

Nā, me whakaoti te whārite x=\frac{-12±2\sqrt{26}}{10} ina he tāpiri te ±. Tāpiri -12 ki te 2\sqrt{26}.

$$x=\frac{2\sqrt{26}-12}{10}$$

Whakawehe -12+2\sqrt{26} ki te 10.

$$x=\frac{\sqrt{26}-6}{5}$$

Nā, me whakaoti te whārite x=\frac{-12±2\sqrt{26}}{10} ina he tango te ±. Tango 2\sqrt{26} mai i -12.

$$x=\frac{-2\sqrt{26}-12}{10}$$

Whakawehe -12-2\sqrt{26} ki te 10.

$$x=\frac{-\sqrt{26}-6}{5}$$

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{-6+\sqrt{26}}{5} mō te x_{1} me te \frac{-6-\sqrt{26}}{5} mō te x_{2}.

$$5x^{2}+12x+2=5\left(x-\frac{\sqrt{26}-6}{5}\right)\left(x-\frac{-\sqrt{26}-6}{5}\right)$$