Solve for x
x=\frac{118455359078051916563803951486093011267876770521240512800069}{1558334187683122846608767340464764566236794791146894845050000}\approx 0.076014092
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945=\frac{500x\left(1-1.042^{-21}\right)}{0.042}+\frac{1000}{1.042^{21}}
Divide 1000x by 2 to get 500x.
945=\frac{500x\left(1-\frac{476837158203125000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}\right)}{0.042}+\frac{1000}{1.042^{21}}
Calculate 1.042 to the power of -21 and get \frac{476837158203125000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}.
945=\frac{500x\times \frac{654500358826911595575682282995201117819453812281695834921}{1131337517030036595575682282995201117819453812281695834921}}{0.042}+\frac{1000}{1.042^{21}}
Subtract \frac{476837158203125000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921} from 1 to get \frac{654500358826911595575682282995201117819453812281695834921}{1131337517030036595575682282995201117819453812281695834921}.
945=\frac{\frac{327250179413455797787841141497600558909726906140847917460500}{1131337517030036595575682282995201117819453812281695834921}x}{0.042}+\frac{1000}{1.042^{21}}
Multiply 500 and \frac{654500358826911595575682282995201117819453812281695834921}{1131337517030036595575682282995201117819453812281695834921} to get \frac{327250179413455797787841141497600558909726906140847917460500}{1131337517030036595575682282995201117819453812281695834921}.
945=\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{1000}{1.042^{21}}
Divide \frac{327250179413455797787841141497600558909726906140847917460500}{1131337517030036595575682282995201117819453812281695834921}x by 0.042 to get \frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x.
945=\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{1000}{2.372586736514575306484733251147952014637303201334182983596244992}
Calculate 1.042 to the power of 21 and get 2.372586736514575306484733251147952014637303201334182983596244992.
945=\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{1000000000000000000000000000000000000000000000000000000000000000000}{2372586736514575306484733251147952014637303201334182983596244992}
Expand \frac{1000}{2.372586736514575306484733251147952014637303201334182983596244992} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000000000000000000000000000000.
945=\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}
Reduce the fraction \frac{1000000000000000000000000000000000000000000000000000000000000000000}{2372586736514575306484733251147952014637303201334182983596244992} to lowest terms by extracting and canceling out 2097152.
\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x+\frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}=945
Swap sides so that all variable terms are on the left hand side.
\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x=945-\frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921}
Subtract \frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921} from both sides.
\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}x=\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}
Subtract \frac{476837158203125000000000000000000000000000000000000000000000}{1131337517030036595575682282995201117819453812281695834921} from 945 to get \frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}.
x=\frac{\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}}{\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}}
Divide both sides by \frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}.
x=\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921\times \frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}}
Express \frac{\frac{592276795390259582819019757430465056339383852606202564000345}{1131337517030036595575682282995201117819453812281695834921}}{\frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921}} as a single fraction.
x=\frac{592276795390259582819019757430465056339383852606202564000345}{7791670938415614233043836702323822831183973955734474225250000}
Multiply 1131337517030036595575682282995201117819453812281695834921 and \frac{7791670938415614233043836702323822831183973955734474225250000}{1131337517030036595575682282995201117819453812281695834921} to get 7791670938415614233043836702323822831183973955734474225250000.
x=\frac{118455359078051916563803951486093011267876770521240512800069}{1558334187683122846608767340464764566236794791146894845050000}
Reduce the fraction \frac{592276795390259582819019757430465056339383852606202564000345}{7791670938415614233043836702323822831183973955734474225250000} to lowest terms by extracting and canceling out 5.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}