Whakaoti i te 4x^2+48x+45

$$4 { x }^{ 2 } +48x+45$$

Tauwehe

$$4\left(x-\left(-\frac{3\sqrt{11}}{2}-6\right)\right)\left(x-\left(\frac{3\sqrt{11}}{2}-6\right)\right)$$

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.

$$4x^{2}+48x+45=0$$

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.

$$x=\frac{-48±\sqrt{48^{2}-4\times 4\times 45}}{2\times 4}$$

Pūrua 48.

$$x=\frac{-48±\sqrt{2304-4\times 4\times 45}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-48±\sqrt{2304-16\times 45}}{2\times 4}$$

Whakareatia -16 ki te 45.

$$x=\frac{-48±\sqrt{2304-720}}{2\times 4}$$

Tāpiri 2304 ki te -720.

$$x=\frac{-48±\sqrt{1584}}{2\times 4}$$

Tuhia te pūtakerua o te 1584.

$$x=\frac{-48±12\sqrt{11}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-48±12\sqrt{11}}{8}$$

Nā, me whakaoti te whārite x=\frac{-48±12\sqrt{11}}{8} ina he tāpiri te ±. Tāpiri -48 ki te 12\sqrt{11}.

$$x=\frac{12\sqrt{11}-48}{8}$$

Whakawehe -48+12\sqrt{11} ki te 8.

$$x=\frac{3\sqrt{11}}{2}-6$$

Nā, me whakaoti te whārite x=\frac{-48±12\sqrt{11}}{8} ina he tango te ±. Tango 12\sqrt{11} mai i -48.

$$x=\frac{-12\sqrt{11}-48}{8}$$

Whakawehe -48-12\sqrt{11} ki te 8.

$$x=-\frac{3\sqrt{11}}{2}-6$$

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 -6+\frac{3\sqrt{11}}{2} mō te x_{1} me te -6-\frac{3\sqrt{11}}{2} mō te x_{2}.

$$4x^{2}+48x+45=4\left(x-\left(\frac{3\sqrt{11}}{2}-6\right)\right)\left(x-\left(-\frac{3\sqrt{11}}{2}-6\right)\right)$$

Aromātai

$$4x^{2}+48x+45$$