Whakaoti i te 2x-sqrt{-x}+3=0

$$2x- \sqrt{ -x } +3 = 0$$

Whakaoti mō x

$$x=-1$$

Ngā Upane Otinga

Me tango 2x+3 mai i ngā taha e rua o te whārite.

$$-\sqrt{-x}=-\left(2x+3\right)$$

Me whakakore te -1 ki ngā taha e rua.

$$\sqrt{-x}=2x+3$$

Pūruatia ngā taha e rua o te whārite.

$$\left(\sqrt{-x}\right)^{2}=\left(2x+3\right)^{2}$$

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

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

Whakamahia te ture huarua \left(a+b\right)^{2}=a^{2}+2ab+b^{2} hei whakaroha \left(2x+3\right)^{2}.

$$-x=4x^{2}+12x+9$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$-x-4x^{2}=12x+9$$

Tangohia te 12x mai i ngā taha e rua.

$$-x-4x^{2}-12x=9$$

Tangohia te 9 mai i ngā taha e rua.

$$-x-4x^{2}-12x-9=0$$

Pahekotia te -x me -12x, ka -13x.

$$-13x-4x^{2}-9=0$$

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

$$-4x^{2}-13x-9=0$$

Hei whakaoti i te whārite, whakatauwehea te taha mauī mā te whakarōpū. Tuatahi, me tuhi anō te taha mauī hei -4x^{2}+ax+bx-9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-13 ab=-4\left(-9\right)=36$$

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 36.

$$-1,-36 -2,-18 -3,-12 -4,-9 -6,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-36=-37 -2-18=-20 -3-12=-15 -4-9=-13 -6-6=-12$$

Ko te otinga te takirua ka hoatu i te tapeke -13.

$$a=-4 b=-9$$

Tuhia anō te -4x^{2}-13x-9 hei \left(-4x^{2}-4x\right)+\left(-9x-9\right).

$$\left(-4x^{2}-4x\right)+\left(-9x-9\right)$$

Tauwehea te 4x i te tuatahi me te 9 i te rōpū tuarua.

$$4x\left(-x-1\right)+9\left(-x-1\right)$$

Whakatauwehea atu te kīanga pātahi -x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-x-1\right)\left(4x+9\right)$$

Hei kimi otinga whārite, me whakaoti te -x-1=0 me te 4x+9=0.

$$x=-1 x=-\frac{9}{4}$$

Whakakapia te -1 mō te x i te whārite 2x-\sqrt{-x}+3=0.

$$2\left(-1\right)-\sqrt{-\left(-1\right)}+3=0$$

Whakarūnātia. Ko te uara x=-1 kua ngata te whārite.

$$0=0$$

Whakakapia te -\frac{9}{4} mō te x i te whārite 2x-\sqrt{-x}+3=0.

$$2\left(-\frac{9}{4}\right)-\sqrt{-\left(-\frac{9}{4}\right)}+3=0$$

Whakarūnātia. Ko te uara x=-\frac{9}{4} kāore e ngata ana ki te whārite.

$$-3=0$$

Ko te whārite \sqrt{-x}=2x+3 he rongoā ahurei.

$$x=-1$$