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

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

p खातीर सोडोवचें

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

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

क्वॉड्रेटिक सिध्दांत वापरून पांवडे

\frac{1}{1000} मेळोवंक -3 चो 10 पॉवर मेजचो.

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

\frac{261}{250} मेळोवंक 1044 आनी \frac{1}{1000} गुणचें.

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

2478968175 मेळोवंक 83145 आनी 29815 गुणचें.

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

\frac{1}{1000000} मेळोवंक -6 चो 10 पॉवर मेजचो.

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

\frac{93}{500000} मेळोवंक 186 आनी \frac{1}{1000000} गुणचें.

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

\frac{1}{100000000} मेळोवंक -8 चो 10 पॉवर मेजचो.

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

\frac{53}{50000000} मेळोवंक 106 आनी \frac{1}{100000000} गुणचें.

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

1-\frac{93}{500000}p+\frac{53}{50000000}p^{2} न 2478968175 गुणपाक विभाजक विशमाचो वापर करचो.

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

दोनूय कुशींतल्यान 2478968175 वजा करचें.

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

दोनूय वटांनी \frac{9221761611}{20000}p जोडचे.

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

\frac{9221782491}{20000}p मेळोवंक \frac{261}{250}p आनी \frac{9221761611}{20000}p एकठांय करचें.

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

दोनूय कुशींतल्यान \frac{5255412531}{2000000}p^{2} वजा करचें.

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

फॉर्म ax^{2}+bx+c=0 चीं सगळीं समिकरणां क्वॉड्रेटिक सिध्दांत: \frac{-b±\sqrt{b^{2}-4ac}}{2a} वापरून सोडोवंक शकतात. क्वॉड्रेटिक सिध्दांत दोन सोडोवणी दितात, एक जेन्ना ± बेरीज आसा आनी एक जेन्ना ती वजा आसता.

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

हें समिकरण प्रमाणित पद्दतीन आसा: ax^{2}+bx+c=0. क्वॉड्रेटिक सिध्दांत \frac{-b±\sqrt{b^{2}-4ac}}{2a} त a खातीर -\frac{5255412531}{2000000}, b खातीर \frac{9221782491}{20000} आनी c खातीर -2478968175 बदली घेवचे.

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

अपूर्णांकांचो गणक आनी भाजक हांकां दोनांकूय वर्गमूळ लावन \frac{9221782491}{20000} क वर्गमूळ लावचें.

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

-\frac{5255412531}{2000000}क -4 फावटी गुणचें.

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

-2478968175क \frac{5255412531}{500000} फावटी गुणचें.

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

सामान्य भाजक सोदून आनी गणकांची बेरीज करून -\frac{521120016433808037}{20000} क \frac{85041272311314165081}{400000000} ची बेरीज करची. मागीर शक्य आसा जाल्यार सगल्यांत ल्हान संज्ञेन अपुर्णांक उणो करचो.

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

-\frac{10337359056364846574919}{400000000} चें वर्गमूळ घेवचें.

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

-\frac{5255412531}{2000000}क 2 फावटी गुणचें.

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

जेन्ना ± अदीक आस्ता तेन्ना समिकरण p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{-\frac{5255412531}{1000000}} सोडोवचें. \frac{3i\sqrt{1148595450707205174991}}{20000} कडेन -\frac{9221782491}{20000} ची बेरीज करची.

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

-\frac{5255412531}{1000000} च्या पुरकाक \frac{-9221782491+3i\sqrt{1148595450707205174991}}{20000} गुणून -\frac{5255412531}{1000000} न \frac{-9221782491+3i\sqrt{1148595450707205174991}}{20000} क भाग लावचो.

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

जेन्ना ± वजा आस्ता तेन्ना समिकरण p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{-\frac{5255412531}{1000000}} सोडोवचें. -\frac{9221782491}{20000} तल्यान \frac{3i\sqrt{1148595450707205174991}}{20000} वजा करची.

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

-\frac{5255412531}{1000000} च्या पुरकाक \frac{-9221782491-3i\sqrt{1148595450707205174991}}{20000} गुणून -\frac{5255412531}{1000000} न \frac{-9221782491-3i\sqrt{1148595450707205174991}}{20000} क भाग लावचो.

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

समिकरण आतां सुटावें जालें.

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

वर्ग पुराय करूंक पांवडे

\frac{1}{1000} मेळोवंक -3 चो 10 पॉवर मेजचो.

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

\frac{261}{250} मेळोवंक 1044 आनी \frac{1}{1000} गुणचें.

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

2478968175 मेळोवंक 83145 आनी 29815 गुणचें.

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

\frac{1}{1000000} मेळोवंक -6 चो 10 पॉवर मेजचो.

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

\frac{93}{500000} मेळोवंक 186 आनी \frac{1}{1000000} गुणचें.

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

\frac{1}{100000000} मेळोवंक -8 चो 10 पॉवर मेजचो.

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

\frac{53}{50000000} मेळोवंक 106 आनी \frac{1}{100000000} गुणचें.

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

1-\frac{93}{500000}p+\frac{53}{50000000}p^{2} न 2478968175 गुणपाक विभाजक विशमाचो वापर करचो.

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

दोनूय वटांनी \frac{9221761611}{20000}p जोडचे.

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

\frac{9221782491}{20000}p मेळोवंक \frac{261}{250}p आनी \frac{9221761611}{20000}p एकठांय करचें.

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

दोनूय कुशींतल्यान \frac{5255412531}{2000000}p^{2} वजा करचें.

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

ह्या सारकें क्वॉड्रेटिक समिकरण वर्ग पुराय करून सोडोवंक शकतात. वर्ग पुराय करूंक, समिकरण x^{2}+bx=c स्वरूपांत आसूंक जाय.

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

-\frac{5255412531}{2000000} वरवीं समिकरणाच्या दोनूय कुशींक भाग लावचो, अपुर्णांकाच्या पुरका वरवीं दोनूय कुशींक गुणपा सारकेंच हें आसता.

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

-\frac{5255412531}{2000000} वरवीं भागाकार केल्यार -\frac{5255412531}{2000000} वरवीं केल्लो गुणाकार काडटा.

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

-\frac{5255412531}{2000000} च्या पुरकाक \frac{9221782491}{20000} गुणून -\frac{5255412531}{2000000} न \frac{9221782491}{20000} क भाग लावचो.

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

-\frac{5255412531}{2000000} च्या पुरकाक 2478968175 गुणून -\frac{5255412531}{2000000} न 2478968175 क भाग लावचो.

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

-\frac{153696374850}{1751804177} मेळपा खातीर 2 न x संज्ञेचो कोऐफिशियंट आशिल्लो -\frac{307392749700}{1751804177} क भाग लावचो. मागीर समिकरणाच्या दोनूय कुशींनी -\frac{153696374850}{1751804177} च्या वर्गाची बेरीज करची. हो पांवडो समिकरणाचे दावे कुशीक एक जुस्त वर्ग करता.

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

अपूर्णांकांचो गणक आनी भाजक हांकां दोनांकूय वर्गमूळ लावन -\frac{153696374850}{1751804177} क वर्गमूळ लावचें.

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

सामान्य भाजक सोदून आनी गणकांची बेरीज करून \frac{23622575642031712522500}{3068817874554647329} क -\frac{50000000}{53} ची बेरीज करची. मागीर शक्य आसा जाल्यार सगल्यांत ल्हान संज्ञेन अपुर्णांक उणो करचो.

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

गुणकपद p^{2}-\frac{307392749700}{1751804177}p+\frac{23622575642031712522500}{3068817874554647329}. सामान्यपणान, जेन्नाx^{2}+bx+c अचूक वर्ग आसात, तो सदांच\left(x+\frac{b}{2}\right)^{2}गुणकपद करूं येता.

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

समिकरणाच्या दोनूय कुशींनी वर्गमूळ काडचो.

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

सोंपें करचें.

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

समिकरणाच्या दोनूय कुशींतल्यान \frac{153696374850}{1751804177} ची बेरीज करची.

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