Whakaoti i te 3x^2+ax+7=3(x-2)^2+b

$$3 x ^ { 2 } + a x + 7 = 3 ( x - 2 ) ^ { 2 } + b$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=\frac{5+b-12x}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }b=-5\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$3x^{2}+ax+7=3\left(x^{2}-4x+4\right)+b$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}-4x+4.

$$3x^{2}+ax+7=3x^{2}-12x+12+b$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$ax+7=3x^{2}-12x+12+b-3x^{2}$$

Pahekotia te 3x^{2} me -3x^{2}, ka 0.

$$ax+7=-12x+12+b$$

Tangohia te 7 mai i ngā taha e rua.

$$ax=-12x+12+b-7$$

Tangohia te 7 i te 12, ka 5.

$$ax=-12x+5+b$$

He hanga arowhānui tō te whārite.

$$xa=5+b-12x$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xa}{x}=\frac{5+b-12x}{x}$$

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

$$a=\frac{5+b-12x}{x}$$

Whakaoti mō a

$$\left\{\begin{matrix}a=\frac{5+b-12x}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }b=-5\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$3x^{2}+ax+7=3\left(x^{2}-4x+4\right)+b$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}-4x+4.

$$3x^{2}+ax+7=3x^{2}-12x+12+b$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$ax+7=3x^{2}-12x+12+b-3x^{2}$$

Pahekotia te 3x^{2} me -3x^{2}, ka 0.

$$ax+7=-12x+12+b$$

Tangohia te 7 mai i ngā taha e rua.

$$ax=-12x+12+b-7$$

Tangohia te 7 i te 12, ka 5.

$$ax=-12x+5+b$$

He hanga arowhānui tō te whārite.

$$xa=5+b-12x$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xa}{x}=\frac{5+b-12x}{x}$$

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

$$a=\frac{5+b-12x}{x}$$

Whakaoti mō b

$$b=ax+12x-5$$

Ngā Upane Otinga

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

$$3x^{2}+ax+7=3\left(x^{2}-4x+4\right)+b$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te x^{2}-4x+4.

$$3x^{2}+ax+7=3x^{2}-12x+12+b$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$3x^{2}-12x+12+b=3x^{2}+ax+7$$

Tangohia te 3x^{2} mai i ngā taha e rua.

$$-12x+12+b=3x^{2}+ax+7-3x^{2}$$

Pahekotia te 3x^{2} me -3x^{2}, ka 0.

$$-12x+12+b=ax+7$$

Me tāpiri te 12x ki ngā taha e rua.

$$12+b=ax+7+12x$$

Tangohia te 12 mai i ngā taha e rua.

$$b=ax+7+12x-12$$

Tangohia te 12 i te 7, ka -5.

$$b=ax-5+12x$$