Whakaoti i te x+4sqrt{x}-12=0

$$x + 4 \sqrt { x } - 12 = 0$$

Whakaoti mō x

$$x=4$$

Ngā Upane Otinga

Me tango x-12 mai i ngā taha e rua o te whārite.

$$4\sqrt{x}=-\left(x-12\right)$$

Hei kimi i te tauaro o x-12, kimihia te tauaro o ia taurangi.

$$4\sqrt{x}=-x-\left(-12\right)$$

Ko te tauaro o -12 ko 12.

$$4\sqrt{x}=-x+12$$

Pūruatia ngā taha e rua o te whārite.

$$\left(4\sqrt{x}\right)^{2}=\left(-x+12\right)^{2}$$

Whakarohaina te \left(4\sqrt{x}\right)^{2}.

$$4^{2}\left(\sqrt{x}\right)^{2}=\left(-x+12\right)^{2}$$

Tātaihia te 4 mā te pū o 2, kia riro ko 16.

$$16\left(\sqrt{x}\right)^{2}=\left(-x+12\right)^{2}$$

Tātaihia te \sqrt{x} mā te pū o 2, kia riro ko x.

$$16x=\left(-x+12\right)^{2}$$

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(-x+12\right)^{2}.

$$16x=x^{2}-24x+144$$

Tangohia te x^{2} mai i ngā taha e rua.

$$16x-x^{2}=-24x+144$$

Me tāpiri te 24x ki ngā taha e rua.

$$16x-x^{2}+24x=144$$

Pahekotia te 16x me 24x, ka 40x.

$$40x-x^{2}=144$$

Tangohia te 144 mai i ngā taha e rua.

$$40x-x^{2}-144=0$$

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-x^{2}+40x-144=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx-144. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=40 ab=-\left(-144\right)=144$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 144.

$$1,144 2,72 3,48 4,36 6,24 8,18 9,16 12,12$$

Tātaihia te tapeke mō ia takirua.

$$1+144=145 2+72=74 3+48=51 4+36=40 6+24=30 8+18=26 9+16=25 12+12=24$$

Ko te otinga te takirua ka hoatu i te tapeke 40.

$$a=36 b=4$$

Tuhia anō te -x^{2}+40x-144 hei \left(-x^{2}+36x\right)+\left(4x-144\right).

$$\left(-x^{2}+36x\right)+\left(4x-144\right)$$

Tauwehea te -x i te tuatahi me te 4 i te rōpū tuarua.

$$-x\left(x-36\right)+4\left(x-36\right)$$

Whakatauwehea atu te kīanga pātahi x-36 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-36\right)\left(-x+4\right)$$

Hei kimi otinga whārite, me whakaoti te x-36=0 me te -x+4=0.

$$x=36 x=4$$

Whakakapia te 36 mō te x i te whārite x+4\sqrt{x}-12=0.

$$36+4\sqrt{36}-12=0$$

Whakarūnātia. Ko te uara x=36 kāore e ngata ana ki te whārite.

$$48=0$$

Whakakapia te 4 mō te x i te whārite x+4\sqrt{x}-12=0.

$$4+4\sqrt{4}-12=0$$

Whakarūnātia. Ko te uara x=4 kua ngata te whārite.

$$0=0$$

Ko te whārite 4\sqrt{x}=12-x he rongoā ahurei.

$$x=4$$