Whakaoti i te 5x^2+5x-4

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

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

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.

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

Pūrua 5.

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

Whakareatia -4 ki te 5.

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

Whakareatia -20 ki te -4.

$$x=\frac{-5±\sqrt{25+80}}{2\times 5}$$

Tāpiri 25 ki te 80.

$$x=\frac{-5±\sqrt{105}}{2\times 5}$$

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}.

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

Aromātai

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