Solve left(x-325^2right)*250^10+y=965^3*741^20+{521}^50

$$\left( x- { 325 }^{ 2 } \right) \times { 250 }^{ 10 } +y = { 965 }^{ 3 } \cdot { 741 }^{ 20 } + { 521 }^{ 50 }$$

Solve for x

$$x=-\frac{y}{953674316406250000000000}+\frac{3474210826411139407126951474442580359664780804476928999311416195443944186677485998610512288264712360329272704134811276457830900917824063}{476837158203125000000000}$$

Steps for Solving Linear Equation

Calculate 325 to the power of 2 and get 105625.

$$\left(x-105625\right)\times 250^{10}+y=965^{3}\times 741^{20}+521^{50}$$

Calculate 250 to the power of 10 and get 953674316406250000000000.

$$\left(x-105625\right)\times 953674316406250000000000+y=965^{3}\times 741^{20}+521^{50}$$

Use the distributive property to multiply x-105625 by 953674316406250000000000.

$$953674316406250000000000x-100731849670410156250000000000+y=965^{3}\times 741^{20}+521^{50}$$

Calculate 965 to the power of 3 and get 898632125.

$$953674316406250000000000x-100731849670410156250000000000+y=898632125\times 741^{20}+521^{50}$$

Calculate 741 to the power of 20 and get 2490945121336414821799716581865691074454148256480076218801.

$$953674316406250000000000x-100731849670410156250000000000+y=898632125\times 2490945121336414821799716581865691074454148256480076218801+521^{50}$$

Multiply 898632125 and 2490945121336414821799716581865691074454148256480076218801 to get 2238443307644925291195375636359702434830264462785735912663107582125.

$$953674316406250000000000x-100731849670410156250000000000+y=2238443307644925291195375636359702434830264462785735912663107582125+521^{50}$$

Calculate 521 to the power of 50 and get 6948421652822278814253902948885160719329561608953857998622832390887886134911664352295733381153788360956110477273310096769592888728066001.

$$953674316406250000000000x-100731849670410156250000000000+y=2238443307644925291195375636359702434830264462785735912663107582125+6948421652822278814253902948885160719329561608953857998622832390887886134911664352295733381153788360956110477273310096769592888728066001$$

Add 2238443307644925291195375636359702434830264462785735912663107582125 and 6948421652822278814253902948885160719329561608953857998622832390887886134911664352295733381153788360956110477273310096769592888728066001 to get 6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545307537772882505505551835648126.

$$953674316406250000000000x-100731849670410156250000000000+y=6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545307537772882505505551835648126$$

Add 100731849670410156250000000000 to both sides.

$$953674316406250000000000x+y=6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545307537772882505505551835648126+100731849670410156250000000000$$

Add 6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545307537772882505505551835648126 and 100731849670410156250000000000 to get 6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545408269622552915661801835648126.

$$953674316406250000000000x+y=6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545408269622552915661801835648126$$

Subtract y from both sides.

$$953674316406250000000000x=6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545408269622552915661801835648126-y$$

Divide both sides by 953674316406250000000000.

$$\frac{953674316406250000000000x}{953674316406250000000000}=\frac{6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545408269622552915661801835648126-y}{953674316406250000000000}$$

Dividing by 953674316406250000000000 undoes the multiplication by 953674316406250000000000.

$$x=\frac{6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545408269622552915661801835648126-y}{953674316406250000000000}$$

Divide 6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545408269622552915661801835648126-y by 953674316406250000000000.

$$x=-\frac{y}{953674316406250000000000}+\frac{3474210826411139407126951474442580359664780804476928999311416195443944186677485998610512288264712360329272704134811276457830900917824063}{476837158203125000000000}$$

Solve for y

$$y=6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545408269622552915661801835648126-953674316406250000000000x$$

Solution Steps

Calculate 325 to the power of 2 and get 105625.

$$\left(x-105625\right)\times 250^{10}+y=965^{3}\times 741^{20}+521^{50}$$

Calculate 250 to the power of 10 and get 953674316406250000000000.

$$\left(x-105625\right)\times 953674316406250000000000+y=965^{3}\times 741^{20}+521^{50}$$

Use the distributive property to multiply x-105625 by 953674316406250000000000.

$$953674316406250000000000x-100731849670410156250000000000+y=965^{3}\times 741^{20}+521^{50}$$

Calculate 965 to the power of 3 and get 898632125.

$$953674316406250000000000x-100731849670410156250000000000+y=898632125\times 741^{20}+521^{50}$$

Calculate 741 to the power of 20 and get 2490945121336414821799716581865691074454148256480076218801.

$$953674316406250000000000x-100731849670410156250000000000+y=898632125\times 2490945121336414821799716581865691074454148256480076218801+521^{50}$$

Multiply 898632125 and 2490945121336414821799716581865691074454148256480076218801 to get 2238443307644925291195375636359702434830264462785735912663107582125.

$$953674316406250000000000x-100731849670410156250000000000+y=2238443307644925291195375636359702434830264462785735912663107582125+521^{50}$$

Calculate 521 to the power of 50 and get 6948421652822278814253902948885160719329561608953857998622832390887886134911664352295733381153788360956110477273310096769592888728066001.

$$953674316406250000000000x-100731849670410156250000000000+y=2238443307644925291195375636359702434830264462785735912663107582125+6948421652822278814253902948885160719329561608953857998622832390887886134911664352295733381153788360956110477273310096769592888728066001$$

Add 2238443307644925291195375636359702434830264462785735912663107582125 and 6948421652822278814253902948885160719329561608953857998622832390887886134911664352295733381153788360956110477273310096769592888728066001 to get 6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545307537772882505505551835648126.

$$953674316406250000000000x-100731849670410156250000000000+y=6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545307537772882505505551835648126$$

Subtract 953674316406250000000000x from both sides.

$$-100731849670410156250000000000+y=6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545307537772882505505551835648126-953674316406250000000000x$$

Add 100731849670410156250000000000 to both sides.

$$y=6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545307537772882505505551835648126-953674316406250000000000x+100731849670410156250000000000$$

Add 6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545307537772882505505551835648126 and 100731849670410156250000000000 to get 6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545408269622552915661801835648126.

$$y=6948421652822278814253902948885160719329561608953857998622832390887888373354971997221024576529424720658545408269622552915661801835648126-953674316406250000000000x$$