Issolvi 4x^2+12x=4(x+p)^2-q

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

Solvi għal q

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

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+p\right)^{2}.

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

Uża l-propjetà distributtiva biex timmultiplika 4 b'x^{2}+2xp+p^{2}.

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

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

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

Naqqas 4x^{2} miż-żewġ naħat.

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

Ikkombina 4x^{2} u -4x^{2} biex tikseb 0.

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

Naqqas 8xp miż-żewġ naħat.

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

Naqqas 4p^{2} miż-żewġ naħat.

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

L-ekwazzjoni hija f'forma standard.

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

Iddividi ż-żewġ naħat b'-1.

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

Meta tiddividi b'-1 titneħħa l-multiplikazzjoni b'-1.

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

Iddividi 12x-8xp-4p^{2} b'-1.

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

Solvi għal p (complex solution)

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

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

Solvi għal p

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

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