Whakaoti i te x+sqrt{5x+19}=-1

$$x+ \sqrt{ 5x+19 } =-1$$

Whakaoti mō x

$$x=-3$$

Ngā Upane Otinga

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

$$\sqrt{5x+19}=-1-x$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{5x+19}\right)^{2}=\left(-1-x\right)^{2}$$

Tātaihia te \sqrt{5x+19} mā te pū o 2, kia riro ko 5x+19.

$$5x+19=\left(-1-x\right)^{2}$$

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(-1-x\right)^{2}.

$$5x+19=1+2x+x^{2}$$

Tangohia te 1 mai i ngā taha e rua.

$$5x+19-1=2x+x^{2}$$

Tangohia te 1 i te 19, ka 18.

$$5x+18=2x+x^{2}$$

Tangohia te 2x mai i ngā taha e rua.

$$5x+18-2x=x^{2}$$

Pahekotia te 5x me -2x, ka 3x.

$$3x+18=x^{2}$$

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

$$3x+18-x^{2}=0$$

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

$$-x^{2}+3x+18=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -x^{2}+ax+bx+18. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=3 ab=-18=-18$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -18.

$$-1,18 -2,9 -3,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+18=17 -2+9=7 -3+6=3$$

Ko te otinga te takirua ka hoatu i te tapeke 3.

$$a=6 b=-3$$

Tuhia anō te -x^{2}+3x+18 hei \left(-x^{2}+6x\right)+\left(-3x+18\right).

$$\left(-x^{2}+6x\right)+\left(-3x+18\right)$$

Tauwehea te -x i te tuatahi me te -3 i te rōpū tuarua.

$$-x\left(x-6\right)-3\left(x-6\right)$$

Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-6\right)\left(-x-3\right)$$

Hei kimi otinga whārite, me whakaoti te x-6=0 me te -x-3=0.

$$x=6 x=-3$$

Whakakapia te 6 mō te x i te whārite x+\sqrt{5x+19}=-1.

$$6+\sqrt{5\times 6+19}=-1$$

Whakarūnātia. Ko te uara x=6 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$13=-1$$

Whakakapia te -3 mō te x i te whārite x+\sqrt{5x+19}=-1.

$$-3+\sqrt{5\left(-3\right)+19}=-1$$

Whakarūnātia. Ko te uara x=-3 kua ngata te whārite.

$$-1=-1$$

Ko te whārite \sqrt{5x+19}=-x-1 he rongoā ahurei.

$$x=-3$$