Solve for x
x=-\frac{3y}{5}+1600000
Solve for y
y=\frac{8000000-5x}{3}
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\sqrt{\frac{5}{8}x+\frac{3}{8}y}=1000
Divide each term of 5x+3y by 8 to get \frac{5}{8}x+\frac{3}{8}y.
\frac{5}{8}x+\frac{3y}{8}=1000000
Square both sides of the equation.
\frac{5}{8}x+\frac{3y}{8}-\frac{3y}{8}=1000000-\frac{3y}{8}
Subtract \frac{3}{8}y from both sides of the equation.
\frac{5}{8}x=1000000-\frac{3y}{8}
Subtracting \frac{3}{8}y from itself leaves 0.
\frac{5}{8}x=-\frac{3y}{8}+1000000
Subtract \frac{3}{8}y from 1000000.
\frac{\frac{5}{8}x}{\frac{5}{8}}=\frac{-\frac{3y}{8}+1000000}{\frac{5}{8}}
Divide both sides of the equation by \frac{5}{8}, which is the same as multiplying both sides by the reciprocal of the fraction.
x=\frac{-\frac{3y}{8}+1000000}{\frac{5}{8}}
Dividing by \frac{5}{8} undoes the multiplication by \frac{5}{8}.
x=-\frac{3y}{5}+1600000
Divide 1000000-\frac{3y}{8} by \frac{5}{8} by multiplying 1000000-\frac{3y}{8} by the reciprocal of \frac{5}{8}.
\sqrt{\frac{5}{8}x+\frac{3}{8}y}=1000
Divide each term of 5x+3y by 8 to get \frac{5}{8}x+\frac{3}{8}y.
\frac{3}{8}y+\frac{5x}{8}=1000000
Square both sides of the equation.
\frac{3}{8}y+\frac{5x}{8}-\frac{5x}{8}=1000000-\frac{5x}{8}
Subtract \frac{5}{8}x from both sides of the equation.
\frac{3}{8}y=1000000-\frac{5x}{8}
Subtracting \frac{5}{8}x from itself leaves 0.
\frac{3}{8}y=-\frac{5x}{8}+1000000
Subtract \frac{5}{8}x from 1000000.
\frac{\frac{3}{8}y}{\frac{3}{8}}=\frac{-\frac{5x}{8}+1000000}{\frac{3}{8}}
Divide both sides of the equation by \frac{3}{8}, which is the same as multiplying both sides by the reciprocal of the fraction.
y=\frac{-\frac{5x}{8}+1000000}{\frac{3}{8}}
Dividing by \frac{3}{8} undoes the multiplication by \frac{3}{8}.
y=\frac{8000000-5x}{3}
Divide 1000000-\frac{5x}{8} by \frac{3}{8} by multiplying 1000000-\frac{5x}{8} by the reciprocal of \frac{3}{8}.
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{ x } ^ { 2 } - 4 x - 5 = 0
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
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