Whakaoti i te 3/8=4x^2+16-20/2*2x*4

$$\frac { 3 } { 8 } = \frac { 4 x ^ { 2 } + 16 - 20 } { 2 \times 2 x \times 4 }$$

Whakaoti mō x

$$x=-\frac{1}{2}=-0.5$$

$$x=2$$

Ngā Upane Whakamahi Tauwehe Mā te Whakarōpū

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 16x, arā, te tauraro pātahi he tino iti rawa te kitea o 8,2\times 2x\times 4.

$$6x=4x^{2}+16-20$$

Tangohia te 20 i te 16, ka -4.

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

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

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

Me tāpiri te 4 ki ngā taha e rua.

$$6x-4x^{2}+4=0$$

Whakawehea ngā taha e rua ki te 2.

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

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

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

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

$$a+b=3 ab=-2\times 2=-4$$

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 -4.

$$-1,4 -2,2$$

Tātaihia te tapeke mō ia takirua.

$$-1+4=3 -2+2=0$$

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

$$a=4 b=-1$$

Tuhia anō te -2x^{2}+3x+2 hei \left(-2x^{2}+4x\right)+\left(-x+2\right).

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

Whakatauwehea atu 2x i te -2x^{2}+4x.

$$2x\left(-x+2\right)-x+2$$

Whakatauwehea atu te kīanga pātahi -x+2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(-x+2\right)\left(2x+1\right)$$

Hei kimi otinga whārite, me whakaoti te -x+2=0 me te 2x+1=0.

$$x=2 x=-\frac{1}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 16x, arā, te tauraro pātahi he tino iti rawa te kitea o 8,2\times 2x\times 4.

$$6x=4x^{2}+16-20$$

Tangohia te 20 i te 16, ka -4.

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

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

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

Me tāpiri te 4 ki ngā taha e rua.

$$6x-4x^{2}+4=0$$

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.

$$-4x^{2}+6x+4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -4 mō a, 6 mō b, me 4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-4\right)\times 4}}{2\left(-4\right)}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\left(-4\right)\times 4}}{2\left(-4\right)}$$

Whakareatia -4 ki te -4.

$$x=\frac{-6±\sqrt{36+16\times 4}}{2\left(-4\right)}$$

Whakareatia 16 ki te 4.

$$x=\frac{-6±\sqrt{36+64}}{2\left(-4\right)}$$

Tāpiri 36 ki te 64.

$$x=\frac{-6±\sqrt{100}}{2\left(-4\right)}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{-6±10}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{-6±10}{-8}$$

Nā, me whakaoti te whārite x=\frac{-6±10}{-8} ina he tāpiri te ±. Tāpiri -6 ki te 10.

$$x=\frac{4}{-8}$$

Whakahekea te hautanga \frac{4}{-8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=-\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±10}{-8} ina he tango te ±. Tango 10 mai i -6.

$$x=-\frac{16}{-8}$$

Whakawehe -16 ki te -8.

$$x=2$$

Kua oti te whārite te whakatau.

$$x=-\frac{1}{2} x=2$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 16x, arā, te tauraro pātahi he tino iti rawa te kitea o 8,2\times 2x\times 4.

$$6x=4x^{2}+16-20$$

Tangohia te 20 i te 16, ka -4.

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

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

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

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

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

Whakawehea ngā taha e rua ki te -4.

$$\frac{-4x^{2}+6x}{-4}=-\frac{4}{-4}$$

Mā te whakawehe ki te -4 ka wetekia te whakareanga ki te -4.

$$x^{2}+\frac{6}{-4}x=-\frac{4}{-4}$$

Whakahekea te hautanga \frac{6}{-4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}-\frac{3}{2}x=-\frac{4}{-4}$$

Whakawehe -4 ki te -4.

$$x^{2}-\frac{3}{2}x=1$$

Whakawehea te -\frac{3}{2}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{3}{4}. Nā, tāpiria te pūrua o te -\frac{3}{4} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}-\frac{3}{2}x+\left(-\frac{3}{4}\right)^{2}=1+\left(-\frac{3}{4}\right)^{2}$$

Pūruatia -\frac{3}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}-\frac{3}{2}x+\frac{9}{16}=1+\frac{9}{16}$$

Tāpiri 1 ki te \frac{9}{16}.

$$x^{2}-\frac{3}{2}x+\frac{9}{16}=\frac{25}{16}$$

Tauwehea x^{2}-\frac{3}{2}x+\frac{9}{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}.

$$\left(x-\frac{3}{4}\right)^{2}=\frac{25}{16}$$

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

$$\sqrt{\left(x-\frac{3}{4}\right)^{2}}=\sqrt{\frac{25}{16}}$$

Whakarūnātia.

$$x-\frac{3}{4}=\frac{5}{4} x-\frac{3}{4}=-\frac{5}{4}$$

Me tāpiri \frac{3}{4} ki ngā taha e rua o te whārite.

$$x=2 x=-\frac{1}{2}$$