Whakaoti i te 3x^2+72x-55

$$3 x ^ { 2 } + 72 x - 55$$

Tauwehe

$$3\left(x-\left(-\frac{\sqrt{1461}}{3}-12\right)\right)\left(x-\left(\frac{\sqrt{1461}}{3}-12\right)\right)$$

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.

$$3x^{2}+72x-55=0$$

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.

$$x=\frac{-72±\sqrt{72^{2}-4\times 3\left(-55\right)}}{2\times 3}$$

Pūrua 72.

$$x=\frac{-72±\sqrt{5184-4\times 3\left(-55\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-72±\sqrt{5184-12\left(-55\right)}}{2\times 3}$$

Whakareatia -12 ki te -55.

$$x=\frac{-72±\sqrt{5184+660}}{2\times 3}$$

Tāpiri 5184 ki te 660.

$$x=\frac{-72±\sqrt{5844}}{2\times 3}$$

Tuhia te pūtakerua o te 5844.

$$x=\frac{-72±2\sqrt{1461}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-72±2\sqrt{1461}}{6}$$

Nā, me whakaoti te whārite x=\frac{-72±2\sqrt{1461}}{6} ina he tāpiri te ±. Tāpiri -72 ki te 2\sqrt{1461}.

$$x=\frac{2\sqrt{1461}-72}{6}$$

Whakawehe -72+2\sqrt{1461} ki te 6.

$$x=\frac{\sqrt{1461}}{3}-12$$

Nā, me whakaoti te whārite x=\frac{-72±2\sqrt{1461}}{6} ina he tango te ±. Tango 2\sqrt{1461} mai i -72.

$$x=\frac{-2\sqrt{1461}-72}{6}$$

Whakawehe -72-2\sqrt{1461} ki te 6.

$$x=-\frac{\sqrt{1461}}{3}-12$$

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 -12+\frac{\sqrt{1461}}{3} mō te x_{1} me te -12-\frac{\sqrt{1461}}{3} mō te x_{2}.

$$3x^{2}+72x-55=3\left(x-\left(\frac{\sqrt{1461}}{3}-12\right)\right)\left(x-\left(-\frac{\sqrt{1461}}{3}-12\right)\right)$$

Aromātai

$$3x^{2}+72x-55$$