Whakaoti i te 2x^2+2y-12x+8=24

$$2 { x }^{ 2 } +2y-12x+8=24$$

Whakaoti mō y

$$y=8+6x-x^{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$2y-12x+8=24-2x^{2}$$

Me tāpiri te 12x ki ngā taha e rua.

$$2y+8=24-2x^{2}+12x$$

Tangohia te 8 mai i ngā taha e rua.

$$2y=24-2x^{2}+12x-8$$

Tangohia te 8 i te 24, ka 16.

$$2y=16-2x^{2}+12x$$

He hanga arowhānui tō te whārite.

$$2y=16+12x-2x^{2}$$

Whakawehea ngā taha e rua ki te 2.

$$\frac{2y}{2}=\frac{16+12x-2x^{2}}{2}$$

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

$$y=\frac{16+12x-2x^{2}}{2}$$

Whakawehe 16-2x^{2}+12x ki te 2.

$$y=8+6x-x^{2}$$

Whakaoti mō x (complex solution)

$$x=\sqrt{17-y}+3$$

$$x=-\sqrt{17-y}+3$$

Whakaoti mō x

$$x=\sqrt{17-y}+3$$

$$x=-\sqrt{17-y}+3\text{, }y\leq 17$$