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

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

Lahendage ja leidke p

$$p=\frac{153696374850+50\sqrt{1148595450707205174991}i}{1751804177}\approx 87,736047709+967,315156682i$$

$$p=\frac{-50\sqrt{1148595450707205174991}i+153696374850}{1751804177}\approx 87,736047709-967,315156682i$$

Juhised ruutvõrrandi valemi kasutamisel

Arvutage -3 aste 10 ja leidke \frac{1}{1000}.

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

Korrutage 1044 ja \frac{1}{1000}, et leida \frac{261}{250}.

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

Korrutage 83145 ja 29815, et leida 2478968175.

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

Arvutage -6 aste 10 ja leidke \frac{1}{1000000}.

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

Korrutage 186 ja \frac{1}{1000000}, et leida \frac{93}{500000}.

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

Arvutage -8 aste 10 ja leidke \frac{1}{100000000}.

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

Korrutage 106 ja \frac{1}{100000000}, et leida \frac{53}{50000000}.

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

Kasutage distributiivsusomadust, et korrutada 2478968175 ja 1-\frac{93}{500000}p+\frac{53}{50000000}p^{2}.

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

Lahutage mõlemast poolest 2478968175.

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

Liitke \frac{9221761611}{20000}p mõlemale poolele.

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

Kombineerige \frac{261}{250}p ja \frac{9221761611}{20000}p, et leida \frac{9221782491}{20000}p.

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

Lahutage mõlemast poolest \frac{5255412531}{2000000}p^{2}.

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

Kõiki võrrandeid, mis on kujul ax^{2}+bx+c=0, saab lahendada ruutvõrrandi valemiga: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Ruutvõrrandi valem annab kaks lahendit: ühe, kui ± on liitmine, ja teise, kui see on lahutamine.

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

See võrrand on standardkujul: ax^{2}+bx+c=0. Asendage ruutvõrrandis \frac{-b±\sqrt{b^{2}-4ac}}{2a} väärtus a väärtusega -\frac{5255412531}{2000000}, b väärtusega \frac{9221782491}{20000} ja c väärtusega -2478968175.

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

Tõstke \frac{9221782491}{20000} ruutu, tõstes ruutu nii murru lugeja kui ka nimetaja.

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

Korrutage omavahel -4 ja -\frac{5255412531}{2000000}.

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

Korrutage omavahel \frac{5255412531}{500000} ja -2478968175.

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

Liitke \frac{85041272311314165081}{400000000} ja -\frac{521120016433808037}{20000}, leides ühise nimetaja ning liites lugejad. Seejärel taandage murd võimaluse korral vähimale ühiskordsele.

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

Leidke -\frac{10337359056364846574919}{400000000} ruutjuur.

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

Korrutage omavahel 2 ja -\frac{5255412531}{2000000}.

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

Nüüd lahendage võrrand p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{-\frac{5255412531}{1000000}}, kui ± on pluss. Liitke -\frac{9221782491}{20000} ja \frac{3i\sqrt{1148595450707205174991}}{20000}.

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

Jagage \frac{-9221782491+3i\sqrt{1148595450707205174991}}{20000} väärtusega -\frac{5255412531}{1000000}, korrutades \frac{-9221782491+3i\sqrt{1148595450707205174991}}{20000} väärtuse -\frac{5255412531}{1000000} pöördväärtusega.

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

Nüüd lahendage võrrand p=\frac{-\frac{9221782491}{20000}±\frac{3\sqrt{1148595450707205174991}i}{20000}}{-\frac{5255412531}{1000000}}, kui ± on miinus. Lahutage \frac{3i\sqrt{1148595450707205174991}}{20000} väärtusest -\frac{9221782491}{20000}.

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

Jagage \frac{-9221782491-3i\sqrt{1148595450707205174991}}{20000} väärtusega -\frac{5255412531}{1000000}, korrutades \frac{-9221782491-3i\sqrt{1148595450707205174991}}{20000} väärtuse -\frac{5255412531}{1000000} pöördväärtusega.

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

Võrrand on nüüd lahendatud.

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

Juhised mõlema poole ruutu tõstmiseks

Arvutage -3 aste 10 ja leidke \frac{1}{1000}.

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

Korrutage 1044 ja \frac{1}{1000}, et leida \frac{261}{250}.

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

Korrutage 83145 ja 29815, et leida 2478968175.

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

Arvutage -6 aste 10 ja leidke \frac{1}{1000000}.

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

Korrutage 186 ja \frac{1}{1000000}, et leida \frac{93}{500000}.

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

Arvutage -8 aste 10 ja leidke \frac{1}{100000000}.

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

Korrutage 106 ja \frac{1}{100000000}, et leida \frac{53}{50000000}.

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

Kasutage distributiivsusomadust, et korrutada 2478968175 ja 1-\frac{93}{500000}p+\frac{53}{50000000}p^{2}.

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

Liitke \frac{9221761611}{20000}p mõlemale poolele.

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

Kombineerige \frac{261}{250}p ja \frac{9221761611}{20000}p, et leida \frac{9221782491}{20000}p.

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

Lahutage mõlemast poolest \frac{5255412531}{2000000}p^{2}.

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

Ruutvõrrandite (nagu see siin) lahendamiseks tuleb mõlemad pooled ruutu tõsta. Ruutu tõstmiseks peab võrrand olema esmalt kujul x^{2}+bx=c.

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

Jagage võrrandi mõlemad pooled väärtusega -\frac{5255412531}{2000000}, mis on sama nagu mõlema poole korrutamine murru pöördväärtusega.

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

-\frac{5255412531}{2000000}-ga jagamine võtab -\frac{5255412531}{2000000}-ga korrutamise tagasi.

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

Jagage \frac{9221782491}{20000} väärtusega -\frac{5255412531}{2000000}, korrutades \frac{9221782491}{20000} väärtuse -\frac{5255412531}{2000000} pöördväärtusega.

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

Jagage 2478968175 väärtusega -\frac{5255412531}{2000000}, korrutades 2478968175 väärtuse -\frac{5255412531}{2000000} pöördväärtusega.

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

Jagage liikme x kordaja -\frac{307392749700}{1751804177} 2-ga, et leida -\frac{153696374850}{1751804177}. Seejärel liitke -\frac{153696374850}{1751804177} ruut võrrandi mõlemale poolele. Selle tehtega saab võrrandi vasakust poolest täisruut.

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

Tõstke -\frac{153696374850}{1751804177} ruutu, tõstes ruutu nii murru lugeja kui ka nimetaja.

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

Liitke -\frac{50000000}{53} ja \frac{23622575642031712522500}{3068817874554647329}, leides ühise nimetaja ning liites lugejad. Seejärel taandage murd võimaluse korral vähimale ühiskordsele.

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

Lahutage p^{2}-\frac{307392749700}{1751804177}p+\frac{23622575642031712522500}{3068817874554647329}. Kui x^{2}+bx+c on üldiselt täiuslik ruut, saab selle alati teguriteks lahutada kui \left(x+\frac{b}{2}\right)^{2}.

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

Leidke võrrandi mõlema poole ruutjuur.

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

Lihtsustage.

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

Liitke võrrandi mõlema poolega \frac{153696374850}{1751804177}.

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