Whakaoti i te 3ax^2+6x+3=0

$$3 a x ^ { 2 } + 6 x + 3 = 0$$

Whakaoti mō a

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

$$x\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te 6x mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$3ax^{2}+3=-6x$$

Tangohia te 3 mai i ngā taha e rua.

$$3ax^{2}=-6x-3$$

He hanga arowhānui tō te whārite.

$$3x^{2}a=-6x-3$$

Whakawehea ngā taha e rua ki te 3x^{2}.

$$\frac{3x^{2}a}{3x^{2}}=\frac{-6x-3}{3x^{2}}$$

Mā te whakawehe ki te 3x^{2} ka wetekia te whakareanga ki te 3x^{2}.

$$a=\frac{-6x-3}{3x^{2}}$$

Whakawehe -6x-3 ki te 3x^{2}.

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

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{1-a}-1}{a}\text{; }x=-\frac{\sqrt{1-a}+1}{a}\text{, }&a\neq 0\\x=-\frac{1}{2}\text{, }&a=0\end{matrix}\right.$$

Whakaoti mō x

$$\left\{\begin{matrix}x=\frac{\sqrt{1-a}-1}{a}\text{; }x=-\frac{\sqrt{1-a}+1}{a}\text{, }&a\neq 0\text{ and }a\leq 1\\x=-\frac{1}{2}\text{, }&a=0\end{matrix}\right.$$