Solve 945=1000*x*(1-1.042^-21)div0.042+1000div1.042^21

$$945=1000 \times x \times (1- { 1.042 }^{ -21 } ) \div 0.042+1000 \div { 1.042 }^{ 21 }$$

Solve for x

$$x=\frac{118455359078051916563803951486093011267876770521240512800069}{3116668375366245693217534680929529132473589582293789690100000}\approx 0.038007046$$

Steps for Solving Linear Equation

Calculate 1.042 to the power of -21 and get \frac{476837158203125000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}.

$$945=\frac{1000x\left(1-\frac{476837158203125000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}\right)}{0.042}+\frac{1000}{1.042^{21}}$$

Subtract \frac{476837158203125000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921} from 1 to get \frac{654500358826911595575682282995201117819453812281695834921}{1131337517030036595575682282995201117819453812281695834921}.

$$945=\frac{1000x\times \frac{654500358826911595575682282995201117819453812281695834921}{1131337517030036595575682282995201117819453812281695834921}}{0.042}+\frac{1000}{1.042^{21}}$$

Multiply 1000 and \frac{654500358826911595575682282995201117819453812281695834921}{1131337517030036595575682282995201117819453812281695834921} to get \frac{654500358826911595575682282995201117819453812281695834921000}{1131337517030036595575682282995201117819453812281695834921}.

$$945=\frac{\frac{654500358826911595575682282995201117819453812281695834921000}{1131337517030036595575682282995201117819453812281695834921}x}{0.042}+\frac{1000}{1.042^{21}}$$

Divide \frac{654500358826911595575682282995201117819453812281695834921000}{1131337517030036595575682282995201117819453812281695834921}x by 0.042 to get \frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}x.

$$945=\frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{1000}{1.042^{21}}$$

Calculate 1.042 to the power of 21 and get 2.372586736514575306484733251147952014637303201334182983596244992.

$$945=\frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{1000}{2.372586736514575306484733251147952014637303201334182983596244992}$$

Expand \frac{1000}{2.372586736514575306484733251147952014637303201334182983596244992} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000000000000000000000000000000.

$$945=\frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{1000000000000000000000000000000000000000000000000000000000000000000}{2372586736514575306484733251147952014637303201334182983596244992}$$

Reduce the fraction \frac{1000000000000000000000000000000000000000000000000000000000000000000}{2372586736514575306484733251147952014637303201334182983596244992} to lowest terms by extracting and canceling out 2097152.

$$945=\frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}=945$$

Subtract \frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921} from both sides.

$$\frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}x=945-\frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}$$

Subtract \frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921} from 945 to get \frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}.

$$\frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}x=\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}$$

Divide both sides by \frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}.

$$x=\frac{\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}}{\frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}}$$

Express \frac{\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}}{\frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}} as a single fraction.

$$x=\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921\times \frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921}}$$

Multiply 1131337517030036595575682282995201117819453812281695834921 and \frac{15583341876831228466087673404647645662367947911468948450500000}{1131337517030036595575682282995201117819453812281695834921} to get 15583341876831228466087673404647645662367947911468948450500000.

$$x=\frac{592276795390259582819019757430465056339383852606202564000345}{15583341876831228466087673404647645662367947911468948450500000}$$

Reduce the fraction \frac{592276795390259582819019757430465056339383852606202564000345}{15583341876831228466087673404647645662367947911468948450500000} to lowest terms by extracting and canceling out 5.

$$x=\frac{118455359078051916563803951486093011267876770521240512800069}{3116668375366245693217534680929529132473589582293789690100000}$$