Riješi 1212^2=108^2+x^2-2*108*x*cos122^circ

$$1212 ^ { 2 } = 108 ^ { 2 } + x ^ { 2 } - 2 \cdot 108 \cdot x \cdot \cos 122 ^ { \circ }$$

Izračunaj x

$$x = \frac{3 \sqrt{3962010143966813418503407198897729} - 8942387583935331}{156250000000000} = 1151\frac{47363934469280}{156250000000000} \approx 1151,303129181$$

$$x=\frac{-3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000}\approx -1265,765690255$$

Koraci korištenja kvadratne formule

Evaluate trigonometric functions in the problem

$$1212 ^ {2} = 108 ^ {2} + x ^ {2} - 2 \cdot 108 \cdot x \cdot -0,5299192642332048$$

Izračunajte koliko je 2 na 1212 da biste dobili 1468944.

$$1468944=108^{2}+x^{2}-2\times 108x\left(-0,5299192642332048\right)$$

Izračunajte koliko je 2 na 108 da biste dobili 11664.

$$1468944=11664+x^{2}-2\times 108x\left(-0,5299192642332048\right)$$

Pomnožite 2 i 108 da biste dobili 216.

$$1468944=11664+x^{2}-216x\left(-0,5299192642332048\right)$$

Pomnožite 216 i -0,5299192642332048 da biste dobili -114,4625610743722368.

$$1468944=11664+x^{2}-\left(-114,4625610743722368x\right)$$

Broj suprotan broju -114,4625610743722368x jest 114,4625610743722368x.

$$1468944=11664+x^{2}+114,4625610743722368x$$

Zamijenite strane tako da svi izrazi s nepoznanicama budu s lijeve strane.

$$11664+x^{2}+114,4625610743722368x=1468944$$

Oduzmite 1468944 od obiju strana.

$$11664+x^{2}+114,4625610743722368x-1468944=0$$

Oduzmite 1468944 od 11664 da biste dobili -1457280.

$$-1457280+x^{2}+114,4625610743722368x=0$$

Sve jednadžbe oblika ax^{2}+bx+c=0 mogu se riješiti pomoću kvadratne jednadžbe: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadratna jednadžba ima dva rješenja: jedno kad je ± zbrajanje i jedno kad je oduzimanje.

$$x^{2}+114,4625610743722368x-1457280=0$$

Ova je jednadžba u standardnom obliku: ax^{2}+bx+c=0. U kvadratnoj jednadžbi \frac{-b±\sqrt{b^{2}-4ac}}{2a} zamijenite 1 s a, 114,4625610743722368 s b i -1457280 s c.

$$x=\frac{-114,4625610743722368±\sqrt{114,4625610743722368^{2}-4\left(-1457280\right)}}{2}$$

Kvadrirajte 114,4625610743722368 tako da kvadrirate brojnik i nazivnik razlomka.

$$x=\frac{-114,4625610743722368±\sqrt{13101,67788770439438838411920663527424-4\left(-1457280\right)}}{2}$$

Pomnožite -4 i -1457280.

$$x=\frac{-114,4625610743722368±\sqrt{13101,67788770439438838411920663527424+5829120}}{2}$$

Dodaj 13101,67788770439438838411920663527424 broju 5829120.

$$x=\frac{-114,4625610743722368±\sqrt{5842221,67788770439438838411920663527424}}{2}$$

Izračunajte kvadratni korijen od 5842221,67788770439438838411920663527424.

$$x=\frac{-114,4625610743722368±\frac{3\sqrt{3962010143966813418503407198897729}}{78125000000000}}{2}$$

Sada riješite jednadžbu x=\frac{-114,4625610743722368±\frac{3\sqrt{3962010143966813418503407198897729}}{78125000000000}}{2} kad je ± plus. Dodaj -114,4625610743722368 broju \frac{3\sqrt{3962010143966813418503407198897729}}{78125000000000}.

$$x=\frac{3\sqrt{3962010143966813418503407198897729}-8942387583935331}{2\times 78125000000000}$$

Podijelite \frac{-8942387583935331+3\sqrt{3962010143966813418503407198897729}}{78125000000000} s 2.

$$x=\frac{3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000}$$

Sada riješite jednadžbu x=\frac{-114,4625610743722368±\frac{3\sqrt{3962010143966813418503407198897729}}{78125000000000}}{2} kad je ± minus. Oduzmite \frac{3\sqrt{3962010143966813418503407198897729}}{78125000000000} od -114,4625610743722368.

$$x=\frac{-3\sqrt{3962010143966813418503407198897729}-8942387583935331}{2\times 78125000000000}$$

Podijelite \frac{-8942387583935331-3\sqrt{3962010143966813418503407198897729}}{78125000000000} s 2.

$$x=\frac{-3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000}$$

Jednadžba je sada riješena.

$$x=\frac{3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000} x=\frac{-3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000}$$

Koraci za računanje kvadrata

Evaluate trigonometric functions in the problem

$$1212 ^ {2} = 108 ^ {2} + x ^ {2} - 2 \cdot 108 \cdot x \cdot -0.5299192642332048$$

Izračunajte koliko je 2 na 1212 da biste dobili 1468944.

$$1468944=108^{2}+x^{2}-2\times 108x\left(-0.5299192642332048\right)$$

Izračunajte koliko je 2 na 108 da biste dobili 11664.

$$1468944=11664+x^{2}-2\times 108x\left(-0.5299192642332048\right)$$

Pomnožite 2 i 108 da biste dobili 216.

$$1468944=11664+x^{2}-216x\left(-0.5299192642332048\right)$$

Pomnožite 216 i -0.5299192642332048 da biste dobili -114.4625610743722368.

$$1468944=11664+x^{2}-\left(-114.4625610743722368x\right)$$

Broj suprotan broju -114.4625610743722368x jest 114.4625610743722368x.

$$1468944=11664+x^{2}+114.4625610743722368x$$

Zamijenite strane tako da svi izrazi s nepoznanicama budu s lijeve strane.

$$11664+x^{2}+114.4625610743722368x=1468944$$

Oduzmite 11664 od obiju strana.

$$x^{2}+114.4625610743722368x=1468944-11664$$

Oduzmite 11664 od 1468944 da biste dobili 1457280.

$$x^{2}+114.4625610743722368x=1457280$$

Podijelite 114.4625610743722368, koeficijent izraza x, s 2 da biste dobili 57.2312805371861184. Zatim objema stranama jednadžbe pridodajte 57.2312805371861184 na kvadrat. Tim korakom lijeva strana jednadžbe postaje potpuna kvadratna jednadžba.

$$x^{2}+114.4625610743722368x+57.2312805371861184^{2}=1457280+57.2312805371861184^{2}$$

Kvadrirajte 57.2312805371861184 tako da kvadrirate brojnik i nazivnik razlomka.

$$x^{2}+114.4625610743722368x+3275.41947192609859709602980165881856=1457280+3275.41947192609859709602980165881856$$

Dodaj 1457280 broju 3275.41947192609859709602980165881856.

$$x^{2}+114.4625610743722368x+3275.41947192609859709602980165881856=1460555.41947192609859709602980165881856$$

Faktor x^{2}+114.4625610743722368x+3275.41947192609859709602980165881856. Općenito, kada je x^{2}+bx+c savršen kvadrat, uvijek se može uzeti u obzir kao \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+57.2312805371861184\right)^{2}=1460555.41947192609859709602980165881856$$

Izračunajte kvadratni korijen obiju strana jednadžbe.

$$\sqrt{\left(x+57.2312805371861184\right)^{2}}=\sqrt{1460555.41947192609859709602980165881856}$$

Pojednostavnite.

$$x+57.2312805371861184=\frac{3\sqrt{3962010143966813418503407198897729}}{156250000000000} x+57.2312805371861184=-\frac{3\sqrt{3962010143966813418503407198897729}}{156250000000000}$$

Oduzmite 57.2312805371861184 od obiju strana jednadžbe.

$$x=\frac{3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000} x=\frac{-3\sqrt{3962010143966813418503407198897729}-8942387583935331}{156250000000000}$$