Whakaoti i te (2x)^2-2x(-x)-3=-1

$$( 2 x ) ^ { 2 } - 2 x ( - x ) - 3 = - 1$$

Whakaoti mō x

$$x=\frac{\sqrt{3}}{3}\approx 0.577350269$$

$$x=-\frac{\sqrt{3}}{3}\approx -0.577350269$$

Ngā Upane mā te Kimi Pūtakerua

Whakarohaina te \left(2x\right)^{2}.

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Me tāpiri te 3 ki ngā taha e rua.

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

Tāpirihia te -1 ki te 3, ka 2.

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

Whakareatia te x ki te x, ka x^{2}.

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

Whakareatia te -2 ki te -1, ka 2.

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

Pahekotia te 4x^{2} me 2x^{2}, ka 6x^{2}.

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

Whakawehea ngā taha e rua ki te 6.

$$x^{2}=\frac{2}{6}$$

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

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

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

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakarohaina te \left(2x\right)^{2}.

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

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

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

Me tāpiri te 1 ki ngā taha e rua.

$$4x^{2}-2x\left(-x\right)-3+1=0$$

Tāpirihia te -3 ki te 1, ka -2.

$$4x^{2}-2x\left(-x\right)-2=0$$

Whakareatia te x ki te x, ka x^{2}.

$$4x^{2}-2x^{2}\left(-1\right)-2=0$$

Whakareatia te -2 ki te -1, ka 2.

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

Pahekotia te 4x^{2} me 2x^{2}, ka 6x^{2}.

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

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

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-2\right)}}{2\times 6}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-2\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{0±\sqrt{-24\left(-2\right)}}{2\times 6}$$

Whakareatia -24 ki te -2.

$$x=\frac{0±\sqrt{48}}{2\times 6}$$

Tuhia te pūtakerua o te 48.

$$x=\frac{0±4\sqrt{3}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{0±4\sqrt{3}}{12}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{3}}{12} ina he tāpiri te ±.

$$x=\frac{\sqrt{3}}{3}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{3}}{12} ina he tango te ±.

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

Kua oti te whārite te whakatau.

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