Whakaoti i te 1/2x^2+bx+c=0

$$\frac { 1 } { 2 } x ^ { 2 } + b x + c = 0$$

Whakaoti mō b (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te \frac{1}{2}x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$bx+c=-\frac{1}{2}x^{2}$$

Tangohia te c mai i ngā taha e rua.

$$bx=-\frac{1}{2}x^{2}-c$$

He hanga arowhānui tō te whārite.

$$xb=-\frac{x^{2}}{2}-c$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xb}{x}=\frac{-\frac{x^{2}}{2}-c}{x}$$

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

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

Whakawehe -\frac{x^{2}}{2}-c ki te x.

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

Whakaoti mō b

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te \frac{1}{2}x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$bx+c=-\frac{1}{2}x^{2}$$

Tangohia te c mai i ngā taha e rua.

$$bx=-\frac{1}{2}x^{2}-c$$

He hanga arowhānui tō te whārite.

$$xb=-\frac{x^{2}}{2}-c$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xb}{x}=\frac{-\frac{x^{2}}{2}-c}{x}$$

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

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

Whakawehe -\frac{x^{2}}{2}-c ki te x.

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

Whakaoti mō c

$$c=-\frac{x\left(x+2b\right)}{2}$$

Ngā Upane Otinga

Tangohia te \frac{1}{2}x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$bx+c=-\frac{1}{2}x^{2}$$

Tangohia te bx mai i ngā taha e rua.

$$c=-\frac{1}{2}x^{2}-bx$$