Issolvi 1044*10^-3p=83145*29815(1-186*10^-6p+106*10^-8p^2)

$$1044 \times 10 ^ { - 3 } p = 83145 \times 29815 ( 1 - 186 \times 10 ^ { - 6 } p + 106 \times 10 ^ { - 8 } p ^ { 2 } )$$

Solvi għal p

$$p=\frac{153696374850+50\sqrt{1148595450707205174991}i}{1751804177}\approx 87.736047709+967.315156682i$$

$$p=\frac{-50\sqrt{1148595450707205174991}i+153696374850}{1751804177}\approx 87.736047709-967.315156682i$$

Passi għall-Użu tal-Formula Kwadratika

Ikkalkula 10 bil-power ta' -3 u tikseb \frac{1}{1000}.

$$1044\times \frac{1}{1000}p=83145\times 29815\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

Immultiplika 1044 u \frac{1}{1000} biex tikseb \frac{261}{250}.

$$\frac{261}{250}p=83145\times 29815\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

Immultiplika 83145 u 29815 biex tikseb 2478968175.

$$\frac{261}{250}p=2478968175\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

Ikkalkula 10 bil-power ta' -6 u tikseb \frac{1}{1000000}.

$$\frac{261}{250}p=2478968175\left(1-186\times \frac{1}{1000000}p+106\times 10^{-8}p^{2}\right)$$

Immultiplika 186 u \frac{1}{1000000} biex tikseb \frac{93}{500000}.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+106\times 10^{-8}p^{2}\right)$$

Ikkalkula 10 bil-power ta' -8 u tikseb \frac{1}{100000000}.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+106\times \frac{1}{100000000}p^{2}\right)$$

Immultiplika 106 u \frac{1}{100000000} biex tikseb \frac{53}{50000000}.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+\frac{53}{50000000}p^{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2478968175 b'1-\frac{93}{500000}p+\frac{53}{50000000}p^{2}.

$$\frac{261}{250}p=2478968175-\frac{9221761611}{20000}p+\frac{5255412531}{2000000}p^{2}$$

Naqqas 2478968175 miż-żewġ naħat.

$$\frac{261}{250}p-2478968175=-\frac{9221761611}{20000}p+\frac{5255412531}{2000000}p^{2}$$

Żid \frac{9221761611}{20000}p maż-żewġ naħat.

$$\frac{261}{250}p-2478968175+\frac{9221761611}{20000}p=\frac{5255412531}{2000000}p^{2}$$

Ikkombina \frac{261}{250}p u \frac{9221761611}{20000}p biex tikseb \frac{9221782491}{20000}p.

$$\frac{9221782491}{20000}p-2478968175=\frac{5255412531}{2000000}p^{2}$$

Naqqas \frac{5255412531}{2000000}p^{2} miż-żewġ naħat.

$$\frac{9221782491}{20000}p-2478968175-\frac{5255412531}{2000000}p^{2}=0$$

L-ekwazzjonijiet kollha tal-formola ax^{2}+bx+c=0 jistgħu jiġu solvuti permezz tal-formula kwadratika: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Il-formula kwadratika tagħti żewġ soluzzjonijiet, waħda meta ± hija addizzjoni u waħda meta hija tnaqqis.

$$-\frac{5255412531}{2000000}p^{2}+\frac{9221782491}{20000}p-2478968175=0$$

Din l-ekwazzjoni hija fil-forma standard: ax^{2}+bx+c=0. Issostitwixxi -\frac{5255412531}{2000000} għal a, \frac{9221782491}{20000} għal b, u -2478968175 għal c fil-formula kwadratika, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{-\frac{9221782491}{20000}±\sqrt{\left(\frac{9221782491}{20000}\right)^{2}-4\left(-\frac{5255412531}{2000000}\right)\left(-2478968175\right)}}{2\left(-\frac{5255412531}{2000000}\right)}$$

Ikkwadra \frac{9221782491}{20000} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$p=\frac{-\frac{9221782491}{20000}±\sqrt{\frac{85041272311314165081}{400000000}-4\left(-\frac{5255412531}{2000000}\right)\left(-2478968175\right)}}{2\left(-\frac{5255412531}{2000000}\right)}$$

Immultiplika -4 b'-\frac{5255412531}{2000000}.

$$p=\frac{-\frac{9221782491}{20000}±\sqrt{\frac{85041272311314165081}{400000000}+\frac{5255412531}{500000}\left(-2478968175\right)}}{2\left(-\frac{5255412531}{2000000}\right)}$$

Immultiplika \frac{5255412531}{500000} b'-2478968175.

$$p=\frac{-\frac{9221782491}{20000}±\sqrt{\frac{85041272311314165081}{400000000}-\frac{521120016433808037}{20000}}}{2\left(-\frac{5255412531}{2000000}\right)}$$

Żid \frac{85041272311314165081}{400000000} ma' -\frac{521120016433808037}{20000} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$p=\frac{-\frac{9221782491}{20000}±\sqrt{-\frac{10337359056364846574919}{400000000}}}{2\left(-\frac{5255412531}{2000000}\right)}$$

Ħu l-għerq kwadrat ta' -\frac{10337359056364846574919}{400000000}.

$$p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{2\left(-\frac{5255412531}{2000000}\right)}$$

Immultiplika 2 b'-\frac{5255412531}{2000000}.

$$p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{-\frac{5255412531}{1000000}}$$

Issa solvi l-ekwazzjoni p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{-\frac{5255412531}{1000000}} fejn ± hija plus. Żid -\frac{9221782491}{20000} ma' \frac{3i\sqrt{1148595450707205174991}}{20000}.

$$p=\frac{-9221782491+3\sqrt{1148595450707205174991}i}{-\frac{5255412531}{1000000}\times 20000}$$

Iddividi \frac{-9221782491+3i\sqrt{1148595450707205174991}}{20000} b'-\frac{5255412531}{1000000} billi timmultiplika \frac{-9221782491+3i\sqrt{1148595450707205174991}}{20000} bir-reċiproku ta' -\frac{5255412531}{1000000}.

$$p=\frac{-50\sqrt{1148595450707205174991}i+153696374850}{1751804177}$$

Issa solvi l-ekwazzjoni p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{-\frac{5255412531}{1000000}} fejn ± hija minus. Naqqas \frac{3i\sqrt{1148595450707205174991}}{20000} minn -\frac{9221782491}{20000}.

$$p=\frac{-3\sqrt{1148595450707205174991}i-9221782491}{-\frac{5255412531}{1000000}\times 20000}$$

Iddividi \frac{-9221782491-3i\sqrt{1148595450707205174991}}{20000} b'-\frac{5255412531}{1000000} billi timmultiplika \frac{-9221782491-3i\sqrt{1148595450707205174991}}{20000} bir-reċiproku ta' -\frac{5255412531}{1000000}.

$$p=\frac{153696374850+50\sqrt{1148595450707205174991}i}{1751804177}$$

L-ekwazzjoni issa solvuta.

$$p=\frac{-50\sqrt{1148595450707205174991}i+153696374850}{1751804177} p=\frac{153696374850+50\sqrt{1148595450707205174991}i}{1751804177}$$

Passi biex Tikkompleta l-Kwadrat

Ikkalkula 10 bil-power ta' -3 u tikseb \frac{1}{1000}.

$$1044\times \frac{1}{1000}p=83145\times 29815\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

Immultiplika 1044 u \frac{1}{1000} biex tikseb \frac{261}{250}.

$$\frac{261}{250}p=83145\times 29815\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

Immultiplika 83145 u 29815 biex tikseb 2478968175.

$$\frac{261}{250}p=2478968175\left(1-186\times 10^{-6}p+106\times 10^{-8}p^{2}\right)$$

Ikkalkula 10 bil-power ta' -6 u tikseb \frac{1}{1000000}.

$$\frac{261}{250}p=2478968175\left(1-186\times \frac{1}{1000000}p+106\times 10^{-8}p^{2}\right)$$

Immultiplika 186 u \frac{1}{1000000} biex tikseb \frac{93}{500000}.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+106\times 10^{-8}p^{2}\right)$$

Ikkalkula 10 bil-power ta' -8 u tikseb \frac{1}{100000000}.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+106\times \frac{1}{100000000}p^{2}\right)$$

Immultiplika 106 u \frac{1}{100000000} biex tikseb \frac{53}{50000000}.

$$\frac{261}{250}p=2478968175\left(1-\frac{93}{500000}p+\frac{53}{50000000}p^{2}\right)$$

Uża l-propjetà distributtiva biex timmultiplika 2478968175 b'1-\frac{93}{500000}p+\frac{53}{50000000}p^{2}.

$$\frac{261}{250}p=2478968175-\frac{9221761611}{20000}p+\frac{5255412531}{2000000}p^{2}$$

Żid \frac{9221761611}{20000}p maż-żewġ naħat.

$$\frac{261}{250}p+\frac{9221761611}{20000}p=2478968175+\frac{5255412531}{2000000}p^{2}$$

Ikkombina \frac{261}{250}p u \frac{9221761611}{20000}p biex tikseb \frac{9221782491}{20000}p.

$$\frac{9221782491}{20000}p=2478968175+\frac{5255412531}{2000000}p^{2}$$

Naqqas \frac{5255412531}{2000000}p^{2} miż-żewġ naħat.

$$\frac{9221782491}{20000}p-\frac{5255412531}{2000000}p^{2}=2478968175$$

Ekwazzjonijiet kwadratiċi bħal din jistgħu jiġu solvuti billi tikkompleta l-kwadrat. Sabiex tikkompleta l-kwadrat, l-ekwazzjoni l-ewwel trid tkun fil-forma x^{2}+bx=c.

$$-\frac{5255412531}{2000000}p^{2}+\frac{9221782491}{20000}p=2478968175$$

Iddividi ż-żewġ naħat tal-ekwazzjoni b'-\frac{5255412531}{2000000}, li hija l-istess bħal multiplikazzjoni taż-żewġ naħat bir-reċiproku tal-frazzjoni.

$$\frac{-\frac{5255412531}{2000000}p^{2}+\frac{9221782491}{20000}p}{-\frac{5255412531}{2000000}}=\frac{2478968175}{-\frac{5255412531}{2000000}}$$

Meta tiddividi b'-\frac{5255412531}{2000000} titneħħa l-multiplikazzjoni b'-\frac{5255412531}{2000000}.

$$p^{2}+\frac{\frac{9221782491}{20000}}{-\frac{5255412531}{2000000}}p=\frac{2478968175}{-\frac{5255412531}{2000000}}$$

Iddividi \frac{9221782491}{20000} b'-\frac{5255412531}{2000000} billi timmultiplika \frac{9221782491}{20000} bir-reċiproku ta' -\frac{5255412531}{2000000}.

$$p^{2}-\frac{307392749700}{1751804177}p=\frac{2478968175}{-\frac{5255412531}{2000000}}$$

Iddividi 2478968175 b'-\frac{5255412531}{2000000} billi timmultiplika 2478968175 bir-reċiproku ta' -\frac{5255412531}{2000000}.

$$p^{2}-\frac{307392749700}{1751804177}p=-\frac{50000000}{53}$$

Iddividi -\frac{307392749700}{1751804177}, il-koeffiċjent tat-terminu x, b'2 biex tikseb -\frac{153696374850}{1751804177}. Imbagħad żid il-kwadru ta' -\frac{153696374850}{1751804177} maż-żewġ naħat tal-ekwazzjoni. Dan il-pass jagħmel in-naħa tax-xellug tal-ekwazzjoni kwadru perfett.

$$p^{2}-\frac{307392749700}{1751804177}p+\left(-\frac{153696374850}{1751804177}\right)^{2}=-\frac{50000000}{53}+\left(-\frac{153696374850}{1751804177}\right)^{2}$$

Ikkwadra -\frac{153696374850}{1751804177} billi tikkwadra kemm in-numeratur u d-denominatur tal-frazzjoni.

$$p^{2}-\frac{307392749700}{1751804177}p+\frac{23622575642031712522500}{3068817874554647329}=-\frac{50000000}{53}+\frac{23622575642031712522500}{3068817874554647329}$$

Żid -\frac{50000000}{53} ma' \frac{23622575642031712522500}{3068817874554647329} biex issib id-denominatur komuni u żżid in-numeraturi. Imbagħad naqqas il-frazzjoni għat-termini l-aktar baxxi jekk possibbli.

$$p^{2}-\frac{307392749700}{1751804177}p+\frac{23622575642031712522500}{3068817874554647329}=-\frac{2871488626768012937477500}{3068817874554647329}$$

Fattur p^{2}-\frac{307392749700}{1751804177}p+\frac{23622575642031712522500}{3068817874554647329}. B'mod ġenerali, meta x^{2}+bx+c huwa kwadru perfett, dejjem jista' jiġu fatturati bħala \left(x+\frac{b}{2}\right)^{2}.

$$\left(p-\frac{153696374850}{1751804177}\right)^{2}=-\frac{2871488626768012937477500}{3068817874554647329}$$

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

$$\sqrt{\left(p-\frac{153696374850}{1751804177}\right)^{2}}=\sqrt{-\frac{2871488626768012937477500}{3068817874554647329}}$$

Issimplifika.

$$p-\frac{153696374850}{1751804177}=\frac{50\sqrt{1148595450707205174991}i}{1751804177} p-\frac{153696374850}{1751804177}=-\frac{50\sqrt{1148595450707205174991}i}{1751804177}$$

Żid \frac{153696374850}{1751804177} maż-żewġ naħat tal-ekwazzjoni.

$$p=\frac{153696374850+50\sqrt{1148595450707205174991}i}{1751804177} p=\frac{-50\sqrt{1148595450707205174991}i+153696374850}{1751804177}$$