Whakaoti i te 15x^2+12x+9

$$15 { x }^{ 2 } +12x+9$$

Tauwehe

$$3\left(5x^{2}+4x+3\right)$$

Ngā Upane Otinga

Tauwehea te 3. Kāore te pūrau 5x^{2}+4x+3 i whakatauwehea i te mea kāhore ōna pūtake whakahau.

$$3\left(5x^{2}+4x+3\right)$$

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.

$$15x^{2}+12x+9=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 15\times 9}}{2\times 15}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 15\times 9}}{2\times 15}$$

Whakareatia -4 ki te 15.

$$x=\frac{-12±\sqrt{144-60\times 9}}{2\times 15}$$

Whakareatia -60 ki te 9.

$$x=\frac{-12±\sqrt{144-540}}{2\times 15}$$

Tāpiri 144 ki te -540.

$$x=\frac{-12±\sqrt{-396}}{2\times 15}$$

Tā te mea e kore te pūrua o tētahi tau tōraro e tautohutia ki te āpure tūturu, kāhore he rongoā. Kāore e taea te pūrau pūrua te whakatauwehe.

$$15x^{2}+12x+9$$

Aromātai

$$15x^{2}+12x+9$$