Whakaoti i te 3x^2+30x+75

$$3 x ^ { 2 } + 30 x + 75$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(x^{2}+10x+25\right)$$

Whakaarohia te x^{2}+10x+25. Whakamahia te tikanga tātai pūrua pā, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, ina a=x, ina b=5.

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Ngā Upane Whakamahi Tauwehe o te Pūrua Huarua

Ko te tikanga tātai o tēnei huatoru he pūrua huatoru, ka whakareatia pea e tētahi tauwehe pātahi. Ka taea ngā pūrua huatoru te tauwehe mā te kimi i ngā pūtakerua o ngā kīanga tau ārahi, autō hoki.

$$factor(3x^{2}+30x+75)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(3,30,75)=3$$

Tauwehea te 3.

$$3\left(x^{2}+10x+25\right)$$

Kimihia te pūtakerua o te kīanga tau autō, 25.

$$\sqrt{25}=5$$

Ko te pūrua huatoru te pūrua o te huarua ko te tapeke tērā, te huatango rānei o ngā pūtakerua o ngā kīanga tau ārahi, autō hoki, e whakaritea ai te tohu e te tohu o te kīanga tau waenga o te pūrua huatoru.

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

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.

$$3x^{2}+30x+75=0$$

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.

$$x=\frac{-30±\sqrt{30^{2}-4\times 3\times 75}}{2\times 3}$$

Pūrua 30.

$$x=\frac{-30±\sqrt{900-4\times 3\times 75}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-30±\sqrt{900-12\times 75}}{2\times 3}$$

Whakareatia -12 ki te 75.

$$x=\frac{-30±\sqrt{900-900}}{2\times 3}$$

Tāpiri 900 ki te -900.

$$x=\frac{-30±\sqrt{0}}{2\times 3}$$

Tuhia te pūtakerua o te 0.

$$x=\frac{-30±0}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-30±0}{6}$$

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 -5 mō te x_{1} me te -5 mō te x_{2}.

$$3x^{2}+30x+75=3\left(x-\left(-5\right)\right)\left(x-\left(-5\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$3x^{2}+30x+75=3\left(x+5\right)\left(x+5\right)$$

Aromātai

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