Whakaoti i te (3-x/2)^2+5-y/4=0

$$( \frac { 3 - x } { 2 } ) ^ { 2 } + \frac { 5 - y } { 4 } = 0$$

Whakaoti mō y

$$y=\left(x-3\right)^{2}+5$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te 4.

$$4\times \left(\frac{3-x}{2}\right)^{2}+5-y=0$$

Kia whakarewa i te \frac{3-x}{2} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$4\times \frac{\left(3-x\right)^{2}}{2^{2}}+5-y=0$$

Tuhia te 4\times \frac{\left(3-x\right)^{2}}{2^{2}} hei hautanga kotahi.

$$\frac{4\left(3-x\right)^{2}}{2^{2}}+5-y=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 5-y ki te \frac{2^{2}}{2^{2}}.

$$\frac{4\left(3-x\right)^{2}}{2^{2}}+\frac{\left(5-y\right)\times 2^{2}}{2^{2}}=0$$

Tā te mea he rite te tauraro o \frac{4\left(3-x\right)^{2}}{2^{2}} me \frac{\left(5-y\right)\times 2^{2}}{2^{2}}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{4\left(3-x\right)^{2}+\left(5-y\right)\times 2^{2}}{2^{2}}=0$$

Mahia ngā whakarea i roto o 4\left(3-x\right)^{2}+\left(5-y\right)\times 2^{2}.

$$\frac{36-24x+4x^{2}+20-4y}{2^{2}}=0$$

Whakakotahitia ngā kupu rite i 36-24x+4x^{2}+20-4y.

$$\frac{56-24x+4x^{2}-4y}{2^{2}}=0$$

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

$$\frac{56-24x+4x^{2}-4y}{4}=0$$

Whakawehea ia wā o 56-24x+4x^{2}-4y ki te 4, kia riro ko 14-6x+x^{2}-y.

$$14-6x+x^{2}-y=0$$

Tangohia te 14 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-6x+x^{2}-y=-14$$

Me tāpiri te 6x ki ngā taha e rua.

$$x^{2}-y=-14+6x$$

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

$$-y=-14+6x-x^{2}$$

He hanga arowhānui tō te whārite.

$$-y=-x^{2}+6x-14$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-y}{-1}=\frac{-x^{2}+6x-14}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$y=\frac{-x^{2}+6x-14}{-1}$$

Whakawehe -14+6x-x^{2} ki te -1.

$$y=x^{2}-6x+14$$

Whakaoti mō x (complex solution)

$$x=\sqrt{y-5}+3$$

$$x=-\sqrt{y-5}+3$$

Whakaoti mō x

$$x=\sqrt{y-5}+3$$

$$x=-\sqrt{y-5}+3\text{, }y\geq 5$$