Issolvi x^2+2xleft(a+1right)=left(x-aright)^2+2left(x+aright)+1

$${ x }^{ 2 } +2x \left( a+1 \right) = { \left(x-a \right) }^{ 2 } +2 \left( x+a \right) +1$$

Solvi għal x

$$x=\frac{\left(a+1\right)^{2}}{4a}$$

$$a\neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża l-propjetà distributtiva biex timmultiplika 2x b'a+1.

$$x^{2}+2xa+2x=\left(x-a\right)^{2}+2\left(x+a\right)+1$$

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

$$x^{2}+2xa+2x=x^{2}-2xa+a^{2}+2\left(x+a\right)+1$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'x+a.

$$x^{2}+2xa+2x=x^{2}-2xa+a^{2}+2x+2a+1$$

Naqqas x^{2} miż-żewġ naħat.

$$x^{2}+2xa+2x-x^{2}=-2xa+a^{2}+2x+2a+1$$

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

$$2xa+2x=-2xa+a^{2}+2x+2a+1$$

Żid 2xa maż-żewġ naħat.

$$2xa+2x+2xa=a^{2}+2x+2a+1$$

Ikkombina 2xa u 2xa biex tikseb 4xa.

$$4xa+2x=a^{2}+2x+2a+1$$

Naqqas 2x miż-żewġ naħat.

$$4xa+2x-2x=a^{2}+2a+1$$

Ikkombina 2x u -2x biex tikseb 0.

$$4xa=a^{2}+2a+1$$

L-ekwazzjoni hija f'forma standard.

$$4ax=a^{2}+2a+1$$

Iddividi ż-żewġ naħat b'4a.

$$\frac{4ax}{4a}=\frac{\left(a+1\right)^{2}}{4a}$$

Meta tiddividi b'4a titneħħa l-multiplikazzjoni b'4a.

$$x=\frac{\left(a+1\right)^{2}}{4a}$$

Solvi għal a (complex solution)

$$a=-2\sqrt{x\left(x-1\right)}+2x-1$$

$$a=2\sqrt{x\left(x-1\right)}+2x-1$$

Solvi għal a

$$a=-2\sqrt{x\left(x-1\right)}+2x-1$$

$$a=2\sqrt{x\left(x-1\right)}+2x-1\text{, }x\geq 1\text{ or }x\leq 0$$