Whakaoti i te a^2+bx^2+c=0

$$a ^ { 2 } + b x ^ { 2 } + c = 0$$

Whakaoti mō b (complex solution)

$$\left\{\begin{matrix}b=-\frac{a^{2}+c}{x^{2}}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=-a^{2}\text{ and }x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te a^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Tangohia te c mai i ngā taha e rua.

$$bx^{2}=-a^{2}-c$$

He hanga arowhānui tō te whārite.

$$x^{2}b=-a^{2}-c$$

Whakawehea ngā taha e rua ki te x^{2}.

$$\frac{x^{2}b}{x^{2}}=\frac{-a^{2}-c}{x^{2}}$$

Mā te whakawehe ki te x^{2} ka wetekia te whakareanga ki te x^{2}.

$$b=\frac{-a^{2}-c}{x^{2}}$$

Whakawehe -a^{2}-c ki te x^{2}.

$$b=-\frac{a^{2}+c}{x^{2}}$$

Whakaoti mō b

$$\left\{\begin{matrix}b=-\frac{a^{2}+c}{x^{2}}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=-a^{2}\text{ and }x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te a^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Tangohia te c mai i ngā taha e rua.

$$bx^{2}=-a^{2}-c$$

He hanga arowhānui tō te whārite.

$$x^{2}b=-a^{2}-c$$

Whakawehea ngā taha e rua ki te x^{2}.

$$\frac{x^{2}b}{x^{2}}=\frac{-a^{2}-c}{x^{2}}$$

Mā te whakawehe ki te x^{2} ka wetekia te whakareanga ki te x^{2}.

$$b=\frac{-a^{2}-c}{x^{2}}$$

Whakawehe -a^{2}-c ki te x^{2}.

$$b=-\frac{a^{2}+c}{x^{2}}$$

Whakaoti mō a (complex solution)

$$a=-i\sqrt{bx^{2}+c}$$

$$a=i\sqrt{bx^{2}+c}$$

Whakaoti mō a

$$a=\sqrt{-bx^{2}-c}$$

$$a=-\sqrt{-bx^{2}-c}\text{, }b\leq -\frac{c}{x^{2}}\text{ or }x=0$$