Whakaoti i te 4x^2-184x+2100

$$4 { x }^{ 2 } -184x+2100$$

Tauwehe

$$4\left(x-25\right)\left(x-21\right)$$

Ngā Upane Otinga

Tauwehea te 4.

$$4\left(x^{2}-46x+525\right)$$

Whakaarohia te x^{2}-46x+525. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+525. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-46 ab=1\times 525=525$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 525.

$$-1,-525 -3,-175 -5,-105 -7,-75 -15,-35 -21,-25$$

Tātaihia te tapeke mō ia takirua.

$$-1-525=-526 -3-175=-178 -5-105=-110 -7-75=-82 -15-35=-50 -21-25=-46$$

Ko te otinga te takirua ka hoatu i te tapeke -46.

$$a=-25 b=-21$$

Tuhia anō te x^{2}-46x+525 hei \left(x^{2}-25x\right)+\left(-21x+525\right).

$$\left(x^{2}-25x\right)+\left(-21x+525\right)$$

Tauwehea te x i te tuatahi me te -21 i te rōpū tuarua.

$$x\left(x-25\right)-21\left(x-25\right)$$

Whakatauwehea atu te kīanga pātahi x-25 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-25\right)\left(x-21\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$4\left(x-25\right)\left(x-21\right)$$

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.

$$4x^{2}-184x+2100=0$$

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.

$$x=\frac{-\left(-184\right)±\sqrt{\left(-184\right)^{2}-4\times 4\times 2100}}{2\times 4}$$

Pūrua -184.

$$x=\frac{-\left(-184\right)±\sqrt{33856-4\times 4\times 2100}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-\left(-184\right)±\sqrt{33856-16\times 2100}}{2\times 4}$$

Whakareatia -16 ki te 2100.

$$x=\frac{-\left(-184\right)±\sqrt{33856-33600}}{2\times 4}$$

Tāpiri 33856 ki te -33600.

$$x=\frac{-\left(-184\right)±\sqrt{256}}{2\times 4}$$

Tuhia te pūtakerua o te 256.

$$x=\frac{-\left(-184\right)±16}{2\times 4}$$

Ko te tauaro o -184 ko 184.

$$x=\frac{184±16}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{184±16}{8}$$

Nā, me whakaoti te whārite x=\frac{184±16}{8} ina he tāpiri te ±. Tāpiri 184 ki te 16.

$$x=\frac{200}{8}$$

Whakawehe 200 ki te 8.

$$x=25$$

Nā, me whakaoti te whārite x=\frac{184±16}{8} ina he tango te ±. Tango 16 mai i 184.

$$x=\frac{168}{8}$$

Whakawehe 168 ki te 8.

$$x=21$$

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 25 mō te x_{1} me te 21 mō te x_{2}.

$$4x^{2}-184x+2100=4\left(x-25\right)\left(x-21\right)$$

Aromātai

$$4\left(x-25\right)\left(x-21\right)$$