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

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

Whakaoti mō x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

Ngā Upane mā te Kimi Pūtakerua

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x-1.

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

Me tāpiri te x^{2} ki ngā taha e rua.

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

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te 2x me -2x, ka 0.

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

Me tāpiri te 2 ki ngā taha e rua.

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

Tāpirihia te 3 ki te 2, ka 5.

$$x^{2}=5$$

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

$$x=\sqrt{5} x=-\sqrt{5}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te x-1.

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

Me tāpiri te x^{2} ki ngā taha e rua.

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

Tangohia te 2x mai i ngā taha e rua.

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

Pahekotia te 2x me -2x, ka 0.

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

Tangohia te 3 mai i ngā taha e rua.

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

Tangohia te 3 i te -2, ka -5.

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

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$x^{2}-5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)}}{2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\left(-5\right)}}{2}$$

Whakareatia -4 ki te -5.

$$x=\frac{0±\sqrt{20}}{2}$$

Tuhia te pūtakerua o te 20.

$$x=\frac{0±2\sqrt{5}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{5}}{2} ina he tāpiri te ±.

$$x=\sqrt{5}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{5}}{2} ina he tango te ±.

$$x=-\sqrt{5}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{5} x=-\sqrt{5}$$