Whakaoti i te (a+c)^2=(a-c)^2

$$( a + c ) ^ { 2 } = ( a - c ) ^ { 2 }$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{C}\text{, }&c=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$a^{2}+2ac+c^{2}=\left(a-c\right)^{2}$$

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

$$a^{2}+2ac+c^{2}=a^{2}-2ac+c^{2}$$

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

$$a^{2}+2ac+c^{2}-a^{2}=-2ac+c^{2}$$

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

$$2ac+c^{2}=-2ac+c^{2}$$

Me tāpiri te 2ac ki ngā taha e rua.

$$2ac+c^{2}+2ac=c^{2}$$

Pahekotia te 2ac me 2ac, ka 4ac.

$$4ac+c^{2}=c^{2}$$

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

$$4ac=c^{2}-c^{2}$$

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

$$4ac=0$$

He hanga arowhānui tō te whārite.

$$4ca=0$$

Whakawehe 0 ki te 4c.

$$a=0$$

Whakaoti mō c (complex solution)

$$\left\{\begin{matrix}\\c=0\text{, }&\text{unconditionally}\\c\in \mathrm{C}\text{, }&a=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(p+q\right)^{2}=p^{2}+2pq+q^{2} hei whakaroha \left(a+c\right)^{2}.

$$a^{2}+2ac+c^{2}=\left(a-c\right)^{2}$$

Whakamahia te ture huarua \left(p-q\right)^{2}=p^{2}-2pq+q^{2} hei whakaroha \left(a-c\right)^{2}.

$$a^{2}+2ac+c^{2}=a^{2}-2ac+c^{2}$$

Me tāpiri te 2ac ki ngā taha e rua.

$$a^{2}+2ac+c^{2}+2ac=a^{2}+c^{2}$$

Pahekotia te 2ac me 2ac, ka 4ac.

$$a^{2}+4ac+c^{2}=a^{2}+c^{2}$$

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

$$a^{2}+4ac+c^{2}-c^{2}=a^{2}$$

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

$$a^{2}+4ac=a^{2}$$

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

$$4ac=a^{2}-a^{2}$$

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

$$4ac=0$$

Whakawehe 0 ki te 4a.

$$c=0$$

Whakaoti mō a

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&c=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$a^{2}+2ac+c^{2}=\left(a-c\right)^{2}$$

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

$$a^{2}+2ac+c^{2}=a^{2}-2ac+c^{2}$$

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

$$a^{2}+2ac+c^{2}-a^{2}=-2ac+c^{2}$$

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

$$2ac+c^{2}=-2ac+c^{2}$$

Me tāpiri te 2ac ki ngā taha e rua.

$$2ac+c^{2}+2ac=c^{2}$$

Pahekotia te 2ac me 2ac, ka 4ac.

$$4ac+c^{2}=c^{2}$$

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

$$4ac=c^{2}-c^{2}$$

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

$$4ac=0$$

He hanga arowhānui tō te whārite.

$$4ca=0$$

Whakawehe 0 ki te 4c.

$$a=0$$

Whakaoti mō c

$$\left\{\begin{matrix}\\c=0\text{, }&\text{unconditionally}\\c\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(p+q\right)^{2}=p^{2}+2pq+q^{2} hei whakaroha \left(a+c\right)^{2}.

$$a^{2}+2ac+c^{2}=\left(a-c\right)^{2}$$

Whakamahia te ture huarua \left(p-q\right)^{2}=p^{2}-2pq+q^{2} hei whakaroha \left(a-c\right)^{2}.

$$a^{2}+2ac+c^{2}=a^{2}-2ac+c^{2}$$

Me tāpiri te 2ac ki ngā taha e rua.

$$a^{2}+2ac+c^{2}+2ac=a^{2}+c^{2}$$

Pahekotia te 2ac me 2ac, ka 4ac.

$$a^{2}+4ac+c^{2}=a^{2}+c^{2}$$

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

$$a^{2}+4ac+c^{2}-c^{2}=a^{2}$$

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

$$a^{2}+4ac=a^{2}$$

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

$$4ac=a^{2}-a^{2}$$

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

$$4ac=0$$

Whakawehe 0 ki te 4a.

$$c=0$$