Whakaoti i te (x)=2x^2-2x-4

$$( x ) = 2 x ^ { 2 } - 2 x - 4$$

Whakaoti mō x

$$x = \frac{\sqrt{41} + 3}{4} \approx 2.350781059$$

$$x=\frac{3-\sqrt{41}}{4}\approx -0.850781059$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

Me tāpiri te 2x ki ngā taha e rua.

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

Pahekotia te x me 2x, ka 3x.

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

Me tāpiri te 4 ki ngā taha e rua.

$$3x-2x^{2}+4=0$$

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.

$$-2x^{2}+3x+4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 3 mō b, me 4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\left(-2\right)\times 4}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-3±\sqrt{9+8\times 4}}{2\left(-2\right)}$$

Whakareatia 8 ki te 4.

$$x=\frac{-3±\sqrt{9+32}}{2\left(-2\right)}$$

Tāpiri 9 ki te 32.

$$x=\frac{-3±\sqrt{41}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-3±\sqrt{41}}{-4}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{41}}{-4} ina he tāpiri te ±. Tāpiri -3 ki te \sqrt{41}.

$$x=\frac{\sqrt{41}-3}{-4}$$

Whakawehe -3+\sqrt{41} ki te -4.

$$x=\frac{3-\sqrt{41}}{4}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{41}}{-4} ina he tango te ±. Tango \sqrt{41} mai i -3.

$$x=\frac{-\sqrt{41}-3}{-4}$$

Whakawehe -3-\sqrt{41} ki te -4.

$$x=\frac{\sqrt{41}+3}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{3-\sqrt{41}}{4} x=\frac{\sqrt{41}+3}{4}$$

Ngā Upane mō te Whakaoti i te Pūrua

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

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

Me tāpiri te 2x ki ngā taha e rua.

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

Pahekotia te x me 2x, ka 3x.

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

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.

$$-2x^{2}+3x=-4$$

Whakawehea ngā taha e rua ki te -2.

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

Mā te whakawehe ki te -2 ka wetekia te whakareanga ki te -2.

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

Whakawehe 3 ki te -2.

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

Whakawehe -4 ki te -2.

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

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.

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

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

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

Tāpiri 2 ki te \frac{9}{16}.

$$x^{2}-\frac{3}{2}x+\frac{9}{16}=\frac{41}{16}$$

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}.

$$\left(x-\frac{3}{4}\right)^{2}=\frac{41}{16}$$

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

$$\sqrt{\left(x-\frac{3}{4}\right)^{2}}=\sqrt{\frac{41}{16}}$$

Whakarūnātia.

$$x-\frac{3}{4}=\frac{\sqrt{41}}{4} x-\frac{3}{4}=-\frac{\sqrt{41}}{4}$$

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

$$x=\frac{\sqrt{41}+3}{4} x=\frac{3-\sqrt{41}}{4}$$