Whakaoti i te 3x^2-2-8x^2+6+5x

$$3 x ^ { 2 } - 2 - 8 x ^ { 2 } + 6 + 5 x$$

Aromātai

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

Ngā Upane Otinga

Pahekotia te 3x^{2} me -8x^{2}, ka -5x^{2}.

$$-5x^{2}-2+6+5x$$

Tāpirihia te -2 ki te 6, ka 4.

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

Tauwehe

$$-5\left(x-\left(-\frac{\sqrt{105}}{10}+\frac{1}{2}\right)\right)\left(x-\left(\frac{\sqrt{105}}{10}+\frac{1}{2}\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 3x^{2} me -8x^{2}, ka -5x^{2}.

$$factor(-5x^{2}-2+6+5x)$$

Tāpirihia te -2 ki te 6, ka 4.

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

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.

$$-5x^{2}+5x+4=0$$

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.

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

Pūrua 5.

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

Whakareatia -4 ki te -5.

$$x=\frac{-5±\sqrt{25+20\times 4}}{2\left(-5\right)}$$

Whakareatia 20 ki te 4.

$$x=\frac{-5±\sqrt{25+80}}{2\left(-5\right)}$$

Tāpiri 25 ki te 80.

$$x=\frac{-5±\sqrt{105}}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$x=\frac{-5±\sqrt{105}}{-10}$$

Nā, me whakaoti te whārite x=\frac{-5±\sqrt{105}}{-10} ina he tāpiri te ±. Tāpiri -5 ki te \sqrt{105}.

$$x=\frac{\sqrt{105}-5}{-10}$$

Whakawehe -5+\sqrt{105} ki te -10.

$$x=-\frac{\sqrt{105}}{10}+\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±\sqrt{105}}{-10} ina he tango te ±. Tango \sqrt{105} mai i -5.

$$x=\frac{-\sqrt{105}-5}{-10}$$

Whakawehe -5-\sqrt{105} ki te -10.

$$x=\frac{\sqrt{105}}{10}+\frac{1}{2}$$

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{1}{2}-\frac{\sqrt{105}}{10} mō te x_{1} me te \frac{1}{2}+\frac{\sqrt{105}}{10} mō te x_{2}.

$$-5x^{2}+5x+4=-5\left(x-\left(-\frac{\sqrt{105}}{10}+\frac{1}{2}\right)\right)\left(x-\left(\frac{\sqrt{105}}{10}+\frac{1}{2}\right)\right)$$