Whakaoti i te 4x^2-2yx+25=left(2x-5right)^2

$$4 { x }^{ 2 } -2yx+25= { \left(2x-5 \right) }^{ 2 }$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=10\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x-5\right)^{2}.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$4x^{2}-2yx+25-4x^{2}=-20x+25$$

Pahekotia te 4x^{2} me -4x^{2}, ka 0.

$$-2yx+25=-20x+25$$

Me tāpiri te 20x ki ngā taha e rua.

$$-2yx+25+20x=25$$

Tangohia te 25 mai i ngā taha e rua.

$$-2yx+20x=25-25$$

Tangohia te 25 i te 25, ka 0.

$$-2yx+20x=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(-2y+20\right)x=0$$

He hanga arowhānui tō te whārite.

$$\left(20-2y\right)x=0$$

Whakawehe 0 ki te -2y+20.

$$x=0$$

Whakaoti mō y (complex solution)

$$\left\{\begin{matrix}\\y=10\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x-5\right)^{2}.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$-2yx+25=4x^{2}-20x+25-4x^{2}$$

Pahekotia te 4x^{2} me -4x^{2}, ka 0.

$$-2yx+25=-20x+25$$

Tangohia te 25 mai i ngā taha e rua.

$$-2yx=-20x+25-25$$

Tangohia te 25 i te 25, ka 0.

$$-2yx=-20x$$

He hanga arowhānui tō te whārite.

$$\left(-2x\right)y=-20x$$

Whakawehea ngā taha e rua ki te -2x.

$$\frac{\left(-2x\right)y}{-2x}=-\frac{20x}{-2x}$$

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

$$y=-\frac{20x}{-2x}$$

Whakawehe -20x ki te -2x.

$$y=10$$

Whakaoti mō x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=10\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x-5\right)^{2}.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$4x^{2}-2yx+25-4x^{2}=-20x+25$$

Pahekotia te 4x^{2} me -4x^{2}, ka 0.

$$-2yx+25=-20x+25$$

Me tāpiri te 20x ki ngā taha e rua.

$$-2yx+25+20x=25$$

Tangohia te 25 mai i ngā taha e rua.

$$-2yx+20x=25-25$$

Tangohia te 25 i te 25, ka 0.

$$-2yx+20x=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te x.

$$\left(-2y+20\right)x=0$$

He hanga arowhānui tō te whārite.

$$\left(20-2y\right)x=0$$

Whakawehe 0 ki te -2y+20.

$$x=0$$

Whakaoti mō y

$$\left\{\begin{matrix}\\y=10\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(a-b\right)^{2}=a^{2}-2ab+b^{2} hei whakaroha \left(2x-5\right)^{2}.

$$4x^{2}-2yx+25=4x^{2}-20x+25$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$-2yx+25=4x^{2}-20x+25-4x^{2}$$

Pahekotia te 4x^{2} me -4x^{2}, ka 0.

$$-2yx+25=-20x+25$$

Tangohia te 25 mai i ngā taha e rua.

$$-2yx=-20x+25-25$$

Tangohia te 25 i te 25, ka 0.

$$-2yx=-20x$$

He hanga arowhānui tō te whārite.

$$\left(-2x\right)y=-20x$$

Whakawehea ngā taha e rua ki te -2x.

$$\frac{\left(-2x\right)y}{-2x}=-\frac{20x}{-2x}$$

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

$$y=-\frac{20x}{-2x}$$

Whakawehe -20x ki te -2x.

$$y=10$$