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

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

Whakaoti mō b

$$b=-a\left(2x+a\right)+2x-7$$

Ngā Upane Otinga

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

$$x^{2}+2x-7=x^{2}+2xa+a^{2}+b$$

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

$$x^{2}+2xa+a^{2}+b=x^{2}+2x-7$$

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

$$2xa+a^{2}+b=x^{2}+2x-7-x^{2}$$

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

$$2xa+a^{2}+b=2x-7$$

Tangohia te 2xa mai i ngā taha e rua.

$$a^{2}+b=2x-7-2xa$$

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

$$b=2x-7-2xa-a^{2}$$

Whakaoti mō a (complex solution)

$$a=-\left(\sqrt{x^{2}+2x-b-7}+x\right)$$

$$a=\sqrt{x^{2}+2x-b-7}-x$$

Whakaoti mō a

$$a=-\left(\sqrt{x^{2}+2x-b-7}+x\right)$$

$$a=\sqrt{x^{2}+2x-b-7}-x\text{, }b\leq x^{2}+2x-7$$