Whakaoti i te x^2-8x+15=(x-a)^2+b

$$x ^ { 2 } - 8 x + 15 = ( x - a ) ^ { 2 } + b$$

Whakaoti mō b

$$b=a\left(2x-a\right)-8x+15$$

Ngā Upane Otinga

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

$$x^{2}-8x+15=x^{2}-2xa+a^{2}+b$$

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

$$x^{2}-2xa+a^{2}+b=x^{2}-8x+15$$

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

$$-2xa+a^{2}+b=x^{2}-8x+15-x^{2}$$

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

$$-2xa+a^{2}+b=-8x+15$$

Me tāpiri te 2xa ki ngā taha e rua.

$$a^{2}+b=-8x+15+2xa$$

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

$$b=-8x+15+2xa-a^{2}$$

Whakaoti mō a (complex solution)

$$a=\sqrt{x^{2}-8x-b+15}+x$$

$$a=-\sqrt{x^{2}-8x-b+15}+x$$

Whakaoti mō a

$$a=\sqrt{x^{2}-8x-b+15}+x$$

$$a=-\sqrt{x^{2}-8x-b+15}+x\text{, }b\leq x^{2}-8x+15$$