Issolvi x^2/(4-x)(1-x)=13*10^9

$$\frac { x ^ { 2 } } { ( 4 - x ) ( 1 - x ) } = 13 \times 10 ^ { 9 }$$

Solvi għal x

$$x = \frac{20000 \sqrt{950625000130} + 32500000000}{12999999999} \approx 4$$

$$x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999}\approx 1$$

Passi għall-Użu tal-Formula Kwadratika

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri 1,4 billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(x-4\right)\left(x-1\right).

$$x^{2}=13\times 10^{9}\left(x-4\right)\left(x-1\right)$$

Ikkalkula 10 bil-power ta' 9 u tikseb 1000000000.

$$x^{2}=13\times 1000000000\left(x-4\right)\left(x-1\right)$$

Immultiplika 13 u 1000000000 biex tikseb 13000000000.

$$x^{2}=13000000000\left(x-4\right)\left(x-1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 13000000000 b'x-4.

$$x^{2}=\left(13000000000x-52000000000\right)\left(x-1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 13000000000x-52000000000 b'x-1 u kkombina termini simili.

$$x^{2}=13000000000x^{2}-65000000000x+52000000000$$

Naqqas 13000000000x^{2} miż-żewġ naħat.

$$x^{2}-13000000000x^{2}=-65000000000x+52000000000$$

Ikkombina x^{2} u -13000000000x^{2} biex tikseb -12999999999x^{2}.

$$-12999999999x^{2}=-65000000000x+52000000000$$

Żid 65000000000x maż-żewġ naħat.

$$-12999999999x^{2}[phone]x=52000000000$$

Naqqas 52000000000 miż-żewġ naħat.

$$-12999999999x^{2}[phone]x-52000000000=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi -12999999999 għal a, 65000000000 għal b, u -52000000000 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-65000000000±\sqrt{65000000000^{2}-4\left(-12999999999\right)\left(-52000000000\right)}}{2\left(-12999999999\right)}$$

Ikkwadra 65000000000.

$$x=\frac{-65000000000±\sqrt{4225000000000000000000-4\left(-12999999999\right)\left(-52000000000\right)}}{2\left(-12999999999\right)}$$

Immultiplika -4 b'-12999999999.

$$x=\frac{-65000000000±\sqrt{4225000000000000000000+51999999996\left(-52000000000\right)}}{2\left(-12999999999\right)}$$

Immultiplika 51999999996 b'-52000000000.

$$x=\frac{-65000000000±\sqrt{4225000000000000000000-2703999999792000000000}}{2\left(-12999999999\right)}$$

Żid 4225000000000000000000 ma' -2703999999792000000000.

$$x=\frac{-65000000000±\sqrt{1521000000208000000000}}{2\left(-12999999999\right)}$$

Ħu l-għerq kwadrat ta' 1521000000208000000000.

$$x=\frac{-65000000000±40000\sqrt{950625000130}}{2\left(-12999999999\right)}$$

Immultiplika 2 b'-12999999999.

$$x=\frac{-65000000000±40000\sqrt{950625000130}}{-25999999998}$$

Issa solvi l-ekwazzjoni x=\frac{-65000000000±40000\sqrt{950625000130}}{-25999999998} fejn ± hija plus. Żid -65000000000 ma' 40000\sqrt{950625000130}.

$$x=\frac{40000\sqrt{950625000130}-65000000000}{-25999999998}$$

Iddividi -65000000000+40000\sqrt{950625000130} b'-25999999998.

$$x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999}$$

Issa solvi l-ekwazzjoni x=\frac{-65000000000±40000\sqrt{950625000130}}{-25999999998} fejn ± hija minus. Naqqas 40000\sqrt{950625000130} minn -65000000000.

$$x=\frac{-40000\sqrt{950625000130}-65000000000}{-25999999998}$$

Iddividi -65000000000-40000\sqrt{950625000130} b'-25999999998.

$$x=\frac{20000\sqrt{950625000130}[phone]}{12999999999}$$

L-ekwazzjoni issa solvuta.

$$x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999} x=\frac{20000\sqrt{950625000130}[phone]}{12999999999}$$

Passi biex Tikkompleta l-Kwadrat

Il-varjabbli x ma jistax ikun ugwali għal kwalunkwe mill-valuri 1,4 billi d-diviżjoni b'żero mhix definita. Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(x-4\right)\left(x-1\right).

$$x^{2}=13\times 10^{9}\left(x-4\right)\left(x-1\right)$$

Ikkalkula 10 bil-power ta' 9 u tikseb 1000000000.

$$x^{2}=13\times 1000000000\left(x-4\right)\left(x-1\right)$$

Immultiplika 13 u 1000000000 biex tikseb 13000000000.

$$x^{2}=13000000000\left(x-4\right)\left(x-1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 13000000000 b'x-4.

$$x^{2}=\left(13000000000x-52000000000\right)\left(x-1\right)$$

Uża l-propjetà distributtiva biex timmultiplika 13000000000x-52000000000 b'x-1 u kkombina termini simili.

$$x^{2}=13000000000x^{2}-65000000000x+52000000000$$

Naqqas 13000000000x^{2} miż-żewġ naħat.

$$x^{2}-13000000000x^{2}=-65000000000x+52000000000$$

Ikkombina x^{2} u -13000000000x^{2} biex tikseb -12999999999x^{2}.

$$-12999999999x^{2}=-65000000000x+52000000000$$

Żid 65000000000x maż-żewġ naħat.

$$-12999999999x^{2}[phone]x=52000000000$$

Iddividi ż-żewġ naħat b'-12999999999.

$$\frac{-12999999999x^{2}[phone]x}{-12999999999}=\frac{52000000000}{-12999999999}$$

Meta tiddividi b'-12999999999 titneħħa l-multiplikazzjoni b'-12999999999.

$$x^{2}+\frac{65000000000}{-12999999999}x=\frac{52000000000}{-12999999999}$$

Iddividi 65000000000 b'-12999999999.

$$x^{2}-\frac{65000000000}{12999999999}x=\frac{52000000000}{-12999999999}$$

Iddividi 52000000000 b'-12999999999.

$$x^{2}-\frac{65000000000}{12999999999}x=-\frac{52000000000}{12999999999}$$

Iddividi -\frac{65000000000}{12999999999}, il-koeffiċjent tat-terminu x, b'2 biex tikseb -\frac{32500000000}{12999999999}. Imbagħad żid il-kwadru ta' -\frac{32500000000}{12999999999} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$x^{2}-\frac{65000000000}{12999999999}x+\left(-\frac{32500000000}{12999999999}\right)^{2}=-\frac{52000000000}{12999999999}+\left(-\frac{32500000000}{12999999999}\right)^{2}$$

Ikkwadra -\frac{32500000000}{12999999999} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$x^{2}-\frac{65000000000}{12999999999}x+\frac{1056250000000000000000}{168999999974000000001}=-\frac{52000000000}{12999999999}+\frac{1056250000000000000000}{168999999974000000001}$$

Żid -\frac{52000000000}{12999999999} ma' \frac{1056250000000000000000}{168999999974000000001} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$x^{2}-\frac{65000000000}{12999999999}x+\frac{1056250000000000000000}{168999999974000000001}=\frac{380250000052000000000}{168999999974000000001}$$

Fattur x^{2}-\frac{65000000000}{12999999999}x+\frac{1056250000000000000000}{168999999974000000001}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{32500000000}{12999999999}\right)^{2}=\frac{380250000052000000000}{168999999974000000001}$$

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

$$\sqrt{\left(x-\frac{32500000000}{12999999999}\right)^{2}}=\sqrt{\frac{380250000052000000000}{168999999974000000001}}$$

Issimplifika.

$$x-\frac{32500000000}{12999999999}=\frac{20000\sqrt{950625000130}}{12999999999} x-\frac{32500000000}{12999999999}=-\frac{20000\sqrt{950625000130}}{12999999999}$$

Żid \frac{32500000000}{12999999999} maż-żewġ naħat tal-ekwazzjoni.

$$x=\frac{20000\sqrt{950625000130}[phone]}{12999999999} x=\frac{32500000000-20000\sqrt{950625000130}}{12999999999}$$