Whakaoti i te 2x^2+2x-5=x^2-6x+4

$$2 x ^ { 2 } + 2 x - 5 = x ^ { 2 } - 6 x + 4$$

Whakaoti mō x

$$x=-9$$

$$x=1$$

Ngā Upane Whakamahi Tauwehe

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

$$2x^{2}+2x-5-x^{2}=-6x+4$$

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

$$x^{2}+2x-5=-6x+4$$

Me tāpiri te 6x ki ngā taha e rua.

$$x^{2}+2x-5+6x=4$$

Pahekotia te 2x me 6x, ka 8x.

$$x^{2}+8x-5=4$$

Tangohia te 4 mai i ngā taha e rua.

$$x^{2}+8x-5-4=0$$

Tangohia te 4 i te -5, ka -9.

$$x^{2}+8x-9=0$$

Hei whakaoti i te whārite, whakatauwehea te x^{2}+8x-9 mā te whakamahi i te tātai x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=8 ab=-9$$

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 -9.

$$-1,9 -3,3$$

Tātaihia te tapeke mō ia takirua.

$$-1+9=8 -3+3=0$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$a=-1 b=9$$

Me tuhi anō te kīanga whakatauwehe \left(x+a\right)\left(x+b\right) mā ngā uara i tātaihia.

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

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

$$x=1 x=-9$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

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

$$2x^{2}+2x-5-x^{2}=-6x+4$$

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

$$x^{2}+2x-5=-6x+4$$

Me tāpiri te 6x ki ngā taha e rua.

$$x^{2}+2x-5+6x=4$$

Pahekotia te 2x me 6x, ka 8x.

$$x^{2}+8x-5=4$$

Tangohia te 4 mai i ngā taha e rua.

$$x^{2}+8x-5-4=0$$

Tangohia te 4 i te -5, ka -9.

$$x^{2}+8x-9=0$$

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

$$a+b=8 ab=1\left(-9\right)=-9$$

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 -9.

$$-1,9 -3,3$$

Tātaihia te tapeke mō ia takirua.

$$-1+9=8 -3+3=0$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$a=-1 b=9$$

Tuhia anō te x^{2}+8x-9 hei \left(x^{2}-x\right)+\left(9x-9\right).

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

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

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

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

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

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

$$x=1 x=-9$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$2x^{2}+2x-5-x^{2}=-6x+4$$

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

$$x^{2}+2x-5=-6x+4$$

Me tāpiri te 6x ki ngā taha e rua.

$$x^{2}+2x-5+6x=4$$

Pahekotia te 2x me 6x, ka 8x.

$$x^{2}+8x-5=4$$

Tangohia te 4 mai i ngā taha e rua.

$$x^{2}+8x-5-4=0$$

Tangohia te 4 i te -5, ka -9.

$$x^{2}+8x-9=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 8 mō b, me -9 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-9\right)}}{2}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-9\right)}}{2}$$

Whakareatia -4 ki te -9.

$$x=\frac{-8±\sqrt{64+36}}{2}$$

Tāpiri 64 ki te 36.

$$x=\frac{-8±\sqrt{100}}{2}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{-8±10}{2}$$

Nā, me whakaoti te whārite x=\frac{-8±10}{2} ina he tāpiri te ±. Tāpiri -8 ki te 10.

$$x=\frac{2}{2}$$

Whakawehe 2 ki te 2.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{-8±10}{2} ina he tango te ±. Tango 10 mai i -8.

$$x=-\frac{18}{2}$$

Whakawehe -18 ki te 2.

$$x=-9$$

Kua oti te whārite te whakatau.

$$x=1 x=-9$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$2x^{2}+2x-5-x^{2}=-6x+4$$

Pahekotia te 2x^{2} me -x^{2}, ka x^{2}.

$$x^{2}+2x-5=-6x+4$$

Me tāpiri te 6x ki ngā taha e rua.

$$x^{2}+2x-5+6x=4$$

Pahekotia te 2x me 6x, ka 8x.

$$x^{2}+8x-5=4$$

Me tāpiri te 5 ki ngā taha e rua.

$$x^{2}+8x=4+5$$

Tāpirihia te 4 ki te 5, ka 9.

$$x^{2}+8x=9$$

Whakawehea te 8, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te 4. Nā, tāpiria te pūrua o te 4 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+8x+4^{2}=9+4^{2}$$

Pūrua 4.

$$x^{2}+8x+16=9+16$$

Tāpiri 9 ki te 16.

$$x^{2}+8x+16=25$$

Tauwehea x^{2}+8x+16. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+4\right)^{2}=25$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{25}$$

Whakarūnātia.

$$x+4=5 x+4=-5$$

Me tango 4 mai i ngā taha e rua o te whārite.

$$x=1 x=-9$$