Issolvi 1/x+350=2/frac{100x{100+x}+350}

$$\frac{ 1 }{ x+350 } = \frac{ 2 }{ \frac{ 100x }{ 100+x } +350 }$$

Solvi għal x (complex solution)

$$x=\frac{-25\sqrt{31}i-225}{2}\approx -112.5-69.597054535i$$

$$x=\frac{-225+25\sqrt{31}i}{2}\approx -112.5+69.597054535i$$

Passi għall-Użu tal-Formula Kwadratika

Il-varjabbli x ma jistax ikun ugwali għal -350 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x+350.

$$1=\frac{1}{50}\left(x+350\right)\left(700+9x\right)^{-1}\left(100+x\right)\times 2$$

Immultiplika \frac{1}{50} u 2 biex tikseb \frac{1}{25}.

$$1=\frac{1}{25}\left(x+350\right)\left(700+9x\right)^{-1}\left(100+x\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{25} b'x+350.

$$1=\left(\frac{1}{25}x+14\right)\left(700+9x\right)^{-1}\left(100+x\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{25}x+14 b'\left(700+9x\right)^{-1}.

$$1=\left(\frac{1}{25}x\left(700+9x\right)^{-1}+14\left(700+9x\right)^{-1}\right)\left(100+x\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{25}x\left(700+9x\right)^{-1}+14\left(700+9x\right)^{-1} b'100+x u kkombina termini simili.

$$1=18\left(700+9x\right)^{-1}x+\frac{1}{25}\left(700+9x\right)^{-1}x^{2}+1400\left(700+9x\right)^{-1}$$

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

$$18\left(700+9x\right)^{-1}x+\frac{1}{25}\left(700+9x\right)^{-1}x^{2}+1400\left(700+9x\right)^{-1}=1$$

Naqqas 1 miż-żewġ naħat.

$$18\left(700+9x\right)^{-1}x+\frac{1}{25}\left(700+9x\right)^{-1}x^{2}+1400\left(700+9x\right)^{-1}-1=0$$

Erġa' ordna t-termini.

$$\frac{1}{25}\times \frac{1}{9x+700}x^{2}+18\times \frac{1}{9x+700}x-1+1400\times \frac{1}{9x+700}=0$$

Il-varjabbli x ma jistax ikun ugwali għal -\frac{700}{9} billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'25\left(9x+700\right), l-inqas denominatur komuni ta' 25,9x+700.

$$\frac{1}{25}\times 25\times 1x^{2}+18\times 25\times 1x+25\left(9x+700\right)\left(-1\right)+1400\times 25\times 1=0$$

Agħmel il-multiplikazzjonijiet.

$$\frac{1}{25}\times 25\times 1x^{2}+450\times 1x+25\left(9x+700\right)\left(-1\right)+35000\times 1=0$$

Immultiplika \frac{1}{25} u 25 biex tikseb 1.

$$1x^{2}+450\times 1x+25\left(9x+700\right)\left(-1\right)+35000\times 1=0$$

Immultiplika 450 u 1 biex tikseb 450.

$$1x^{2}+450x+25\left(9x+700\right)\left(-1\right)+35000\times 1=0$$

Immultiplika 25 u -1 biex tikseb -25.

$$1x^{2}+450x-25\left(9x+700\right)+35000\times 1=0$$

Uża l-propjetà distributtiva biex timmultiplika -25 b'9x+700.

$$1x^{2}+450x-225x-17500+35000\times 1=0$$

Ikkombina 450x u -225x biex tikseb 225x.

$$1x^{2}+225x-17500+35000\times 1=0$$

Immultiplika 35000 u 1 biex tikseb 35000.

$$1x^{2}+225x-17500+35000=0$$

Żid -17500 u 35000 biex tikseb 17500.

$$1x^{2}+225x+17500=0$$

Erġa' ordna t-termini.

$$x^{2}+225x+17500=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi 1 għal a, 225 għal b, u 17500 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-225±\sqrt{225^{2}-4\times 17500}}{2}$$

Ikkwadra 225.

$$x=\frac{-225±\sqrt{50625-4\times 17500}}{2}$$

Immultiplika -4 b'17500.

$$x=\frac{-225±\sqrt{50625-70000}}{2}$$

Żid 50625 ma' -70000.

$$x=\frac{-225±\sqrt{-19375}}{2}$$

Ħu l-għerq kwadrat ta' -19375.

$$x=\frac{-225±25\sqrt{31}i}{2}$$

Issa solvi l-ekwazzjoni x=\frac{-225±25\sqrt{31}i}{2} fejn ± hija plus. Żid -225 ma' 25i\sqrt{31}.

$$x=\frac{-225+25\sqrt{31}i}{2}$$

Issa solvi l-ekwazzjoni x=\frac{-225±25\sqrt{31}i}{2} fejn ± hija minus. Naqqas 25i\sqrt{31} minn -225.

$$x=\frac{-25\sqrt{31}i-225}{2}$$

L-ekwazzjoni issa solvuta.

$$x=\frac{-225+25\sqrt{31}i}{2} x=\frac{-25\sqrt{31}i-225}{2}$$

Passi biex Tikkompleta l-Kwadrat

Il-varjabbli x ma jistax ikun ugwali għal -350 billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'x+350.

$$1=\frac{1}{50}\left(x+350\right)\left(700+9x\right)^{-1}\left(100+x\right)\times 2$$

Immultiplika \frac{1}{50} u 2 biex tikseb \frac{1}{25}.

$$1=\frac{1}{25}\left(x+350\right)\left(700+9x\right)^{-1}\left(100+x\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{25} b'x+350.

$$1=\left(\frac{1}{25}x+14\right)\left(700+9x\right)^{-1}\left(100+x\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{25}x+14 b'\left(700+9x\right)^{-1}.

$$1=\left(\frac{1}{25}x\left(700+9x\right)^{-1}+14\left(700+9x\right)^{-1}\right)\left(100+x\right)$$

Uża l-propjetà distributtiva biex timmultiplika \frac{1}{25}x\left(700+9x\right)^{-1}+14\left(700+9x\right)^{-1} b'100+x u kkombina termini simili.

$$1=18\left(700+9x\right)^{-1}x+\frac{1}{25}\left(700+9x\right)^{-1}x^{2}+1400\left(700+9x\right)^{-1}$$

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

$$18\left(700+9x\right)^{-1}x+\frac{1}{25}\left(700+9x\right)^{-1}x^{2}+1400\left(700+9x\right)^{-1}=1$$

Erġa' ordna t-termini.

$$\frac{1}{25}\times \frac{1}{9x+700}x^{2}+18\times \frac{1}{9x+700}x+1400\times \frac{1}{9x+700}=1$$

Il-varjabbli x ma jistax ikun ugwali għal -\frac{700}{9} billi d-diviżjoni b'żero mhux iddefinit. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'25\left(9x+700\right), l-inqas denominatur komuni ta' 25,9x+700.

$$\frac{1}{25}\times 25\times 1x^{2}+18\times 25\times 1x+1400\times 25\times 1=25\left(9x+700\right)$$

Agħmel il-multiplikazzjonijiet.

$$\frac{1}{25}\times 25\times 1x^{2}+450\times 1x+35000\times 1=25\left(9x+700\right)$$

Immultiplika \frac{1}{25} u 25 biex tikseb 1.

$$1x^{2}+450\times 1x+35000\times 1=25\left(9x+700\right)$$

Immultiplika 450 u 1 biex tikseb 450.

$$1x^{2}+450x+35000\times 1=25\left(9x+700\right)$$

Immultiplika 35000 u 1 biex tikseb 35000.

$$1x^{2}+450x+35000=25\left(9x+700\right)$$

Uża l-propjetà distributtiva biex timmultiplika 25 b'9x+700.

$$1x^{2}+450x+35000=225x+17500$$

Naqqas 225x miż-żewġ naħat.

$$1x^{2}+450x+35000-225x=17500$$

Ikkombina 450x u -225x biex tikseb 225x.

$$1x^{2}+225x+35000=17500$$

Naqqas 35000 miż-żewġ naħat.

$$1x^{2}+225x=17500-35000$$

Naqqas 35000 minn 17500 biex tikseb -17500.

$$1x^{2}+225x=-17500$$

Erġa' ordna t-termini.

$$x^{2}+225x=-17500$$

Iddividi 225, il-koeffiċjent tat-terminu x, b'2 biex tikseb \frac{225}{2}. Imbagħad żid il-kwadru ta' \frac{225}{2} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}+225x+\left(\frac{225}{2}\right)^{2}=-17500+\left(\frac{225}{2}\right)^{2}$$

Ikkwadra \frac{225}{2} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}+225x+\frac{50625}{4}=-17500+\frac{50625}{4}$$

Żid -17500 ma' \frac{50625}{4}.

$$x^{2}+225x+\frac{50625}{4}=-\frac{19375}{4}$$

Fattur x^{2}+225x+\frac{50625}{4}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{225}{2}\right)^{2}=-\frac{19375}{4}$$

Ħu l-għerq kwadrat taż-żewġ naħat tal-ekwazzjoni.

$$\sqrt{\left(x+\frac{225}{2}\right)^{2}}=\sqrt{-\frac{19375}{4}}$$

Issimplifika.

$$x+\frac{225}{2}=\frac{25\sqrt{31}i}{2} x+\frac{225}{2}=-\frac{25\sqrt{31}i}{2}$$

Naqqas \frac{225}{2} miż-żewġ naħat tal-ekwazzjoni.

$$x=\frac{-225+25\sqrt{31}i}{2} x=\frac{-25\sqrt{31}i-225}{2}$$