Whakaoti i te (7x-a)^2=49x^2-bx+9

$$( 7 x - a ) ^ { 2 } = 49 x ^ { 2 } - b x + 9$$

Whakaoti mō b (complex solution)

$$\left\{\begin{matrix}b=\frac{14ax-a^{2}+9}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&\left(a=-3\text{ or }a=3\right)\text{ and }x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(p-q\right)^{2}=p^{2}-2pq+q^{2} hei whakaroha \left(7x-a\right)^{2}.

$$49x^{2}-14xa+a^{2}=49x^{2}-bx+9$$

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

$$49x^{2}-bx+9=49x^{2}-14xa+a^{2}$$

Tangohia te 49x^{2} mai i ngā taha e rua.

$$-bx+9=49x^{2}-14xa+a^{2}-49x^{2}$$

Pahekotia te 49x^{2} me -49x^{2}, ka 0.

$$-bx+9=-14xa+a^{2}$$

Tangohia te 9 mai i ngā taha e rua.

$$-bx=-14xa+a^{2}-9$$

He hanga arowhānui tō te whārite.

$$\left(-x\right)b=-14ax+a^{2}-9$$

Whakawehea ngā taha e rua ki te -x.

$$\frac{\left(-x\right)b}{-x}=\frac{-14ax+a^{2}-9}{-x}$$

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

$$b=\frac{-14ax+a^{2}-9}{-x}$$

Whakawehe -14xa+a^{2}-9 ki te -x.

$$b=-\frac{-14ax+a^{2}-9}{x}$$

Whakaoti mō b

$$\left\{\begin{matrix}b=\frac{14ax-a^{2}+9}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&x=0\text{ and }|a|=3\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te ture huarua \left(p-q\right)^{2}=p^{2}-2pq+q^{2} hei whakaroha \left(7x-a\right)^{2}.

$$49x^{2}-14xa+a^{2}=49x^{2}-bx+9$$

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

$$49x^{2}-bx+9=49x^{2}-14xa+a^{2}$$

Tangohia te 49x^{2} mai i ngā taha e rua.

$$-bx+9=49x^{2}-14xa+a^{2}-49x^{2}$$

Pahekotia te 49x^{2} me -49x^{2}, ka 0.

$$-bx+9=-14xa+a^{2}$$

Tangohia te 9 mai i ngā taha e rua.

$$-bx=-14xa+a^{2}-9$$

He hanga arowhānui tō te whārite.

$$\left(-x\right)b=-14ax+a^{2}-9$$

Whakawehea ngā taha e rua ki te -x.

$$\frac{\left(-x\right)b}{-x}=\frac{-14ax+a^{2}-9}{-x}$$

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

$$b=\frac{-14ax+a^{2}-9}{-x}$$

Whakawehe -14xa+a^{2}-9 ki te -x.

$$b=-\frac{-14ax+a^{2}-9}{x}$$

Whakaoti mō a (complex solution)

$$a=\sqrt{49x^{2}-bx+9}+7x$$

$$a=-\sqrt{49x^{2}-bx+9}+7x$$