Riješi 592y^2=106856*10^18-5*624*10^99

$$592 y ^ { 2 } = 106856 \times 10 ^ { 18 } - 5 \cdot 624 \times 10 ^ { 9 } 9$$

Riješite za y

$$y = \frac{50000 \sqrt{98841799974026}}{37} \approx 13435028840,779150009$$

$$y = -\frac{50000 \sqrt{98841799974026}}{37} \approx -13435028840,779150009$$

Koraci pronalaženjem kvadratnog korijena

Izračunajte 10 stepen od 18 i dobijte 1000000000000000000.

$$592y^{2}=106856\times 1000000000000000000-5\times 624\times 10^{9}\times 9$$

Pomnožite 106856 i 1000000000000000000 da biste dobili 106856000000000000000000.

$$592y^{2}=106856000000000000000000-5\times 624\times 10^{9}\times 9$$

Pomnožite 5 i 624 da biste dobili 3120.

$$592y^{2}=106856000000000000000000-3120\times 10^{9}\times 9$$

Izračunajte 10 stepen od 9 i dobijte 1000000000.

$$592y^{2}=106856000000000000000000-3120\times 1000000000\times 9$$

Pomnožite 3120 i 1000000000 da biste dobili 3120000000000.

$$592y^{2}=106856000000000000000000-3120000000000\times 9$$

Pomnožite 3120000000000 i 9 da biste dobili 28080000000000.

$$592y^{2}=106856000000000000000000-28080000000000$$

Oduzmite 28080000000000 od 106856000000000000000000 da biste dobili 106855999971920000000000.

$$592y^{2}=106855999971920000000000$$

Podijelite obje strane s 592.

$$y^{2}=\frac{106855999971920000000000}{592}$$

Svedite razlomak \frac{106855999971920000000000}{592} na najprostije elemente rastavlјanjem i kraćenjem 16.

$$y^{2}=\frac{6678499998245000000000}{37}$$

Izračunajte kvadratni korijen od obje strane jednačine.

$$y=\frac{50000\sqrt{98841799974026}}{37} y=-\frac{50000\sqrt{98841799974026}}{37}$$

Koraci pomoću kvadratne formule

Izračunajte 10 stepen od 18 i dobijte 1000000000000000000.

$$592y^{2}=106856\times 1000000000000000000-5\times 624\times 10^{9}\times 9$$

Pomnožite 106856 i 1000000000000000000 da biste dobili 106856000000000000000000.

$$592y^{2}=106856000000000000000000-5\times 624\times 10^{9}\times 9$$

Pomnožite 5 i 624 da biste dobili 3120.

$$592y^{2}=106856000000000000000000-3120\times 10^{9}\times 9$$

Izračunajte 10 stepen od 9 i dobijte 1000000000.

$$592y^{2}=106856000000000000000000-3120\times 1000000000\times 9$$

Pomnožite 3120 i 1000000000 da biste dobili 3120000000000.

$$592y^{2}=106856000000000000000000-3120000000000\times 9$$

Pomnožite 3120000000000 i 9 da biste dobili 28080000000000.

$$592y^{2}=106856000000000000000000-28080000000000$$

Oduzmite 28080000000000 od 106856000000000000000000 da biste dobili 106855999971920000000000.

$$592y^{2}=106855999971920000000000$$

Oduzmite 106855999971920000000000 s obje strane.

$$592y^{2}-106855999971920000000000=0$$

Ova jednačina je u standardnom obliku: ax^{2}+bx+c=0. Zamijenite 592 i a, 0 i b, kao i -106855999971920000000000 i c u kvadratnoj formuli, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 592\left(-106855999971920000000000\right)}}{2\times 592}$$

Izračunajte kvadrat od 0.

$$y=\frac{0±\sqrt{-4\times 592\left(-106855999971920000000000\right)}}{2\times 592}$$

Pomnožite -4 i 592.

$$y=\frac{0±\sqrt{-2368\left(-106855999971920000000000\right)}}{2\times 592}$$

Pomnožite -2368 i -106855999971920000000000.

$$y=\frac{0±\sqrt{253035007933506560000000000}}{2\times 592}$$

Izračunajte kvadratni korijen od 253035007933506560000000000.

$$y=\frac{0±1600000\sqrt{98841799974026}}{2\times 592}$$

Pomnožite 2 i 592.

$$y=\frac{0±1600000\sqrt{98841799974026}}{1184}$$

Sada riješite jednačinu y=\frac{0±1600000\sqrt{98841799974026}}{1184} kada je ± plus.

$$y=\frac{50000\sqrt{98841799974026}}{37}$$

Sada riješite jednačinu y=\frac{0±1600000\sqrt{98841799974026}}{1184} kada je ± minus.

$$y=-\frac{50000\sqrt{98841799974026}}{37}$$

Jednačina je riješena.

$$y=\frac{50000\sqrt{98841799974026}}{37} y=-\frac{50000\sqrt{98841799974026}}{37}$$