Whakaoti i te x^2-4x+9=(x+a)^2+b

$$x ^ { 2 } - 4 x + 9 = ( x + a ) ^ { 2 } + b$$

Whakaoti mō b

$$b=-a\left(2x+a\right)-4x+9$$

Ngā Upane Otinga

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

$$x^{2}-4x+9=x^{2}+2xa+a^{2}+b$$

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

$$x^{2}+2xa+a^{2}+b=x^{2}-4x+9$$

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

$$2xa+a^{2}+b=x^{2}-4x+9-x^{2}$$

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

$$2xa+a^{2}+b=-4x+9$$

Tangohia te 2xa mai i ngā taha e rua.

$$a^{2}+b=-4x+9-2xa$$

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

$$b=-4x+9-2xa-a^{2}$$

Whakaoti mō a (complex solution)

$$a=-\left(\sqrt{x^{2}-4x-b+9}+x\right)$$

$$a=\sqrt{x^{2}-4x-b+9}-x$$

Whakaoti mō a

$$a=-\left(\sqrt{x^{2}-4x-b+9}+x\right)$$

$$a=\sqrt{x^{2}-4x-b+9}-x\text{, }b\leq x^{2}-4x+9$$