Issolvi 1/4=(2k+2)^2-(1-x)/(8-k)^2

$$\frac { 1 } { 4 } = \frac { ( 2 k + 2 ) ^ { 2 } - ( 1 - x ) } { ( 8 - k ) ^ { 2 } }$$

Solvi għal x

$$x=-\frac{15k^{2}}{4}-12k+13$$

$$k\neq 8$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'4\left(k-8\right)^{2}, l-inqas denominatur komuni ta' 4,\left(8-k\right)^{2}.

$$\left(k-8\right)^{2}=4\left(\left(2k+2\right)^{2}-\left(1-x\right)\right)$$

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(k-8\right)^{2}.

$$k^{2}-16k+64=4\left(\left(2k+2\right)^{2}-\left(1-x\right)\right)$$

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

$$k^{2}-16k+64=4\left(4k^{2}+8k+4-\left(1-x\right)\right)$$

Biex issib l-oppost ta' 1-x, sib l-oppost ta' kull terminu.

$$k^{2}-16k+64=4\left(4k^{2}+8k+4-1+x\right)$$

Naqqas 1 minn 4 biex tikseb 3.

$$k^{2}-16k+64=4\left(4k^{2}+8k+3+x\right)$$

Uża l-propjetà distributtiva biex timmultiplika 4 b'4k^{2}+8k+3+x.

$$k^{2}-16k+64=16k^{2}+32k+12+4x$$

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

$$16k^{2}+32k+12+4x=k^{2}-16k+64$$

Naqqas 16k^{2} miż-żewġ naħat.

$$32k+12+4x=k^{2}-16k+64-16k^{2}$$

Ikkombina k^{2} u -16k^{2} biex tikseb -15k^{2}.

$$32k+12+4x=-15k^{2}-16k+64$$

Naqqas 32k miż-żewġ naħat.

$$12+4x=-15k^{2}-16k+64-32k$$

Ikkombina -16k u -32k biex tikseb -48k.

$$12+4x=-15k^{2}-48k+64$$

Naqqas 12 miż-żewġ naħat.

$$4x=-15k^{2}-48k+64-12$$

Naqqas 12 minn 64 biex tikseb 52.

$$4x=-15k^{2}-48k+52$$

L-ekwazzjoni hija f'forma standard.

$$4x=52-48k-15k^{2}$$

Iddividi ż-żewġ naħat b'4.

$$\frac{4x}{4}=\frac{52-48k-15k^{2}}{4}$$

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

$$x=\frac{52-48k-15k^{2}}{4}$$

Iddividi -15k^{2}-48k+52 b'4.

$$x=-\frac{15k^{2}}{4}-12k+13$$

Solvi għal k (complex solution)

$$\left\{\begin{matrix}\\k=-\frac{2\sqrt{339-15x}}{15}-\frac{8}{5}\text{, }&\text{unconditionally}\\k=\frac{2\sqrt{339-15x}}{15}-\frac{8}{5}\text{, }&x\neq -323\end{matrix}\right.$$

Solvi għal k

$$\left\{\begin{matrix}k=\frac{2\sqrt{339-15x}}{15}-\frac{8}{5}\text{, }&x\neq -323\text{ and }x\leq \frac{113}{5}\\k=-\frac{2\sqrt{339-15x}}{15}-\frac{8}{5}\text{, }&x\leq \frac{113}{5}\end{matrix}\right.$$