Question
Solve the equation
Solve for x
Solve for y
x=21+−9−12y−4y2x=21−−9−12y−4y2
Evaluate
2x2+2y2−2x+6y+5=0
Rewrite the expression
2x2+2y2+6y+5−2x=0
Rewrite in standard form
2x2−2x+2y2+6y+5=0
Substitute a=2,b=−2 and c=2y2+6y+5 into the quadratic formula x=2a−b±b2−4ac
x=2×22±(−2)2−4×2(2y2+6y+5)
Simplify the expression
x=42±(−2)2−4×2(2y2+6y+5)
Simplify the expression
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Evaluate
(−2)2−4×2(2y2+6y+5)
Multiply the terms
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Multiply the terms
4×2(2y2+6y+5)
Multiply the terms
8(2y2+6y+5)
Apply the distributive property
8×2y2+8×6y+8×5
Multiply the terms
16y2+8×6y+8×5
Multiply the terms
16y2+48y+8×5
Multiply the numbers
16y2+48y+40
(−2)2−(16y2+48y+40)
Rewrite the expression
22−(16y2+48y+40)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
22−16y2−48y−40
Evaluate the power
4−16y2−48y−40
Subtract the numbers
−36−16y2−48y
x=42±−36−16y2−48y
Simplify the radical expression
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Evaluate
−36−16y2−48y
Factor the expression
4(−9−12y−4y2)
The root of a product is equal to the product of the roots of each factor
4×−9−12y−4y2
Evaluate the root
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Evaluate
4
Write the number in exponential form with the base of 2
22
Reduce the index of the radical and exponent with 2
2
2−9−12y−4y2
x=42±2−9−12y−4y2
Separate the equation into 2 possible cases
x=42+2−9−12y−4y2x=42−2−9−12y−4y2
Simplify the expression
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Evaluate
x=42+2−9−12y−4y2
Divide the terms
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Evaluate
42+2−9−12y−4y2
Rewrite the expression
42(1+−9−12y−4y2)
Cancel out the common factor 2
21+−9−12y−4y2
x=21+−9−12y−4y2
x=21+−9−12y−4y2x=42−2−9−12y−4y2
Solution
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Evaluate
x=42−2−9−12y−4y2
Divide the terms
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Evaluate
42−2−9−12y−4y2
Rewrite the expression
42(1−−9−12y−4y2)
Cancel out the common factor 2
21−−9−12y−4y2
x=21−−9−12y−4y2
x=21+−9−12y−4y2x=21−−9−12y−4y2
Show Solution

Testing for symmetry
Testing for symmetry about the origin
Testing for symmetry about the x-axis
Testing for symmetry about the y-axis
Not symmetry with respect to the origin
Evaluate
2x2+2y2−2x+6y+5=0
To test if the graph of 2x2+2y2−2x+6y+5=0 is symmetry with respect to the origin,substitute -x for x and -y for y
2(−x)2+2(−y)2−2(−x)+6(−y)+5=0
Evaluate
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Evaluate
2(−x)2+2(−y)2−2(−x)+6(−y)+5
Multiply the terms
2x2+2(−y)2−2(−x)+6(−y)+5
Multiply the terms
2x2+2y2−2(−x)+6(−y)+5
Multiply the numbers
2x2+2y2+2x+6(−y)+5
Multiply the numbers
2x2+2y2+2x−6y+5
2x2+2y2+2x−6y+5=0
Solution
Not symmetry with respect to the origin
Show Solution

Rewrite the equation
r=2cos(θ)−3sin(θ)+−9+8sin2(θ)−3sin(2θ)r=2cos(θ)−3sin(θ)−−9+8sin2(θ)−3sin(2θ)
Evaluate
2x2+2y2−2x+6y+5=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
2(cos(θ)×r)2+2(sin(θ)×r)2−2cos(θ)×r+6sin(θ)×r+5=0
Factor the expression
(2cos2(θ)+2sin2(θ))r2+(−2cos(θ)+6sin(θ))r+5=0
Simplify the expression
2r2+(−2cos(θ)+6sin(θ))r+5=0
Solve using the quadratic formula
r=42cos(θ)−6sin(θ)±(−2cos(θ)+6sin(θ))2−4×2×5
Simplify
r=42cos(θ)−6sin(θ)±−36+32sin2(θ)−12sin(2θ)
Separate the equation into 2 possible cases
r=42cos(θ)−6sin(θ)+−36+32sin2(θ)−12sin(2θ)r=42cos(θ)−6sin(θ)−−36+32sin2(θ)−12sin(2θ)
Evaluate
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Evaluate
42cos(θ)−6sin(θ)+−36+32sin2(θ)−12sin(2θ)
Simplify the root
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Evaluate
−36+32sin2(θ)−12sin(2θ)
Factor the expression
4(−9+8sin2(θ)−3sin(2θ))
Write the number in exponential form with the base of 2
22(−9+8sin2(θ)−3sin(2θ))
Calculate
2−9+8sin2(θ)−3sin(2θ)
42cos(θ)−6sin(θ)+2−9+8sin2(θ)−3sin(2θ)
Factor
42(cos(θ)−3sin(θ)+−9+8sin2(θ)−3sin(2θ))
Reduce the fraction
2cos(θ)−3sin(θ)+−9+8sin2(θ)−3sin(2θ)
r=2cos(θ)−3sin(θ)+−9+8sin2(θ)−3sin(2θ)r=42cos(θ)−6sin(θ)−−36+32sin2(θ)−12sin(2θ)
Solution
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Evaluate
42cos(θ)−6sin(θ)−−36+32sin2(θ)−12sin(2θ)
Simplify the root
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Evaluate
−36+32sin2(θ)−12sin(2θ)
Factor the expression
4(−9+8sin2(θ)−3sin(2θ))
Write the number in exponential form with the base of 2
22(−9+8sin2(θ)−3sin(2θ))
Calculate
2−9+8sin2(θ)−3sin(2θ)
42cos(θ)−6sin(θ)−2−9+8sin2(θ)−3sin(2θ)
Factor
42(cos(θ)−3sin(θ)−−9+8sin2(θ)−3sin(2θ))
Reduce the fraction
2cos(θ)−3sin(θ)−−9+8sin2(θ)−3sin(2θ)
r=2cos(θ)−3sin(θ)+−9+8sin2(θ)−3sin(2θ)r=2cos(θ)−3sin(θ)−−9+8sin2(θ)−3sin(2θ)
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=2y+3−2x+1
Calculate
2x2+2y2−2x+6y+5=0
Take the derivative of both sides
dxd(2x2+2y2−2x+6y+5)=dxd(0)
Calculate the derivative
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Evaluate
dxd(2x2+2y2−2x+6y+5)
Use differentiation rules
dxd(2x2)+dxd(2y2)+dxd(−2x)+dxd(6y)+dxd(5)
Evaluate the derivative
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Evaluate
dxd(2x2)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
2×dxd(x2)
Use dxdxn=nxn−1 to find derivative
2×2x
Multiply the terms
4x
4x+dxd(2y2)+dxd(−2x)+dxd(6y)+dxd(5)
Evaluate the derivative
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Evaluate
dxd(2y2)
Use differentiation rules
dyd(2y2)×dxdy
Evaluate the derivative
4ydxdy
4x+4ydxdy+dxd(−2x)+dxd(6y)+dxd(5)
Evaluate the derivative
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Evaluate
dxd(−2x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−2×dxd(x)
Use dxdxn=nxn−1 to find derivative
−2×1
Any expression multiplied by 1 remains the same
−2
4x+4ydxdy−2+dxd(6y)+dxd(5)
Evaluate the derivative
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Evaluate
dxd(6y)
Use differentiation rules
dyd(6y)×dxdy
Evaluate the derivative
6dxdy
4x+4ydxdy−2+6dxdy+dxd(5)
Use dxd(c)=0 to find derivative
4x+4ydxdy−2+6dxdy+0
Evaluate
4x+4ydxdy−2+6dxdy
4x+4ydxdy−2+6dxdy=dxd(0)
Calculate the derivative
4x+4ydxdy−2+6dxdy=0
Collect like terms by calculating the sum or difference of their coefficients
4x−2+(4y+6)dxdy=0
Move the constant to the right side
(4y+6)dxdy=0−(4x−2)
Subtract the terms
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Evaluate
0−(4x−2)
Removing 0 doesn't change the value,so remove it from the expression
−(4x−2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−4x+2
(4y+6)dxdy=−4x+2
Divide both sides
4y+6(4y+6)dxdy=4y+6−4x+2
Divide the numbers
dxdy=4y+6−4x+2
Solution
More Steps

Evaluate
4y+6−4x+2
Rewrite the expression
4y+62(−2x+1)
Rewrite the expression
2(2y+3)2(−2x+1)
Reduce the fraction
2y+3−2x+1
dxdy=2y+3−2x+1
Show Solution
