Whakaoti i te x+(x+2)/2*(x-1)=8

$$\frac { x + ( x + 2 ) } { 2 } \cdot ( x - 1 ) = 8$$

Whakaoti mō x

$$x=-3$$

$$x=3$$

Ngā Upane mā te Kimi Pūtakerua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$\left(x+x+2\right)\left(x-1\right)=16$$

Pahekotia te x me x, ka 2x.

$$\left(2x+2\right)\left(x-1\right)=16$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2x+2 ki ia tau o x-1.

$$2x^{2}-2x+2x-2=16$$

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

$$2x^{2}-2=16$$

Me tāpiri te 2 ki ngā taha e rua.

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

Tāpirihia te 16 ki te 2, ka 18.

$$2x^{2}=18$$

Whakawehea ngā taha e rua ki te 2.

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

Whakawehea te 18 ki te 2, kia riro ko 9.

$$x^{2}=9$$

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

$$x=3 x=-3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia ngā taha e rua o te whārite ki te 2.

$$\left(x+x+2\right)\left(x-1\right)=16$$

Pahekotia te x me x, ka 2x.

$$\left(2x+2\right)\left(x-1\right)=16$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o 2x+2 ki ia tau o x-1.

$$2x^{2}-2x+2x-2=16$$

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

$$2x^{2}-2=16$$

Tangohia te 16 mai i ngā taha e rua.

$$2x^{2}-2-16=0$$

Tangohia te 16 i te -2, ka -18.

$$2x^{2}-18=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 2 mō a, 0 mō b, me -18 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-18\right)}}{2\times 2}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-18\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\left(-18\right)}}{2\times 2}$$

Whakareatia -8 ki te -18.

$$x=\frac{0±\sqrt{144}}{2\times 2}$$

Tuhia te pūtakerua o te 144.

$$x=\frac{0±12}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±12}{4}$$

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

$$x=3$$

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

$$x=-3$$

Kua oti te whārite te whakatau.

$$x=3 x=-3$$