Whakaoti i te 4x^2+12x=4(x+p)^2-q

$$4 x ^ { 2 } + 12 x = 4 ( x + p ) ^ { 2 } - q$$

Whakaoti mō q

$$q=4\left(p\left(2x+p\right)-3x\right)$$

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+p\right)^{2}.

$$4x^{2}+12x=4\left(x^{2}+2xp+p^{2}\right)-q$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te x^{2}+2xp+p^{2}.

$$4x^{2}+12x=4x^{2}+8xp+4p^{2}-q$$

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

$$4x^{2}+8xp+4p^{2}-q=4x^{2}+12x$$

Tangohia te 4x^{2} mai i ngā taha e rua.

$$8xp+4p^{2}-q=4x^{2}+12x-4x^{2}$$

Pahekotia te 4x^{2} me -4x^{2}, ka 0.

$$8xp+4p^{2}-q=12x$$

Tangohia te 8xp mai i ngā taha e rua.

$$4p^{2}-q=12x-8xp$$

Tangohia te 4p^{2} mai i ngā taha e rua.

$$-q=12x-8xp-4p^{2}$$

He hanga arowhānui tō te whārite.

$$-q=-8px+12x-4p^{2}$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-q}{-1}=\frac{-8px+12x-4p^{2}}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$q=\frac{-8px+12x-4p^{2}}{-1}$$

Whakawehe 12x-8xp-4p^{2} ki te -1.

$$q=8px-12x+4p^{2}$$

Whakaoti mō p (complex solution)

$$p=-\frac{\sqrt{4x^{2}+12x+q}}{2}-x$$

$$p=\frac{\sqrt{4x^{2}+12x+q}}{2}-x$$

Whakaoti mō p

$$p=-\frac{\sqrt{4x^{2}+12x+q}}{2}-x$$

$$p=\frac{\sqrt{4x^{2}+12x+q}}{2}-x\text{, }q\geq -4x^{2}-12x$$