Issolvi -left(x-1right)^2+x^2+2x+1+2x=x^2+hx+1

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

Solvi għal h

$$h=-x+6-\frac{1}{x}$$

$$x\neq 0$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(x-1\right)^{2}.

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

Biex issib l-oppost ta' x^{2}-2x+1, sib l-oppost ta' kull terminu.

$$-x^{2}+2x-1+x^{2}+2x+1+2x=x^{2}+hx+1$$

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

$$2x-1+2x+1+2x=x^{2}+hx+1$$

Ikkombina 2x u 2x biex tikseb 4x.

$$4x-1+1+2x=x^{2}+hx+1$$

Żid -1 u 1 biex tikseb 0.

$$4x+2x=x^{2}+hx+1$$

Ikkombina 4x u 2x biex tikseb 6x.

$$6x=x^{2}+hx+1$$

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

$$x^{2}+hx+1=6x$$

Naqqas x^{2} miż-żewġ naħat.

$$hx+1=6x-x^{2}$$

Naqqas 1 miż-żewġ naħat.

$$hx=6x-x^{2}-1$$

L-ekwazzjoni hija f'forma standard.

$$xh=-x^{2}+6x-1$$

Iddividi ż-żewġ naħat b'x.

$$\frac{xh}{x}=\frac{-x^{2}+6x-1}{x}$$

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

$$h=\frac{-x^{2}+6x-1}{x}$$

Iddividi 6x-x^{2}-1 b'x.

$$h=-x+6-\frac{1}{x}$$

Solvi għal x (complex solution)

$$x=\frac{-\sqrt{\left(h-8\right)\left(h-4\right)}-h+6}{2}$$

$$x=\frac{\sqrt{\left(h-8\right)\left(h-4\right)}-h+6}{2}$$

Solvi għal x

$$x=\frac{-\sqrt{\left(h-8\right)\left(h-4\right)}-h+6}{2}$$

$$x=\frac{\sqrt{\left(h-8\right)\left(h-4\right)}-h+6}{2}\text{, }h\leq 4\text{ or }h\geq 8$$