# Solve for y 5y^2+2=0 5y2+2=0
Subtract 2 from both sides of the equation.
5y2=-2
Divide each term by 5 and simplify.
Divide each term in 5y2=-2 by 5.
5y25=-25
Cancel the common factor of 5.
Cancel the common factor.
5y25=-25
Divide y2 by 1.
y2=-25
y2=-25
Move the negative in front of the fraction.
y2=-25
y2=-25
Take the square root of both sides of the equation to eliminate the exponent on the left side.
y=±-25
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Rewrite -1 as i2.
y=±i2(25)
Pull terms out from under the radical.
y=±i25
Rewrite 25 as 25.
y=±i(25)
Multiply 25 by 55.
y=±i(25⋅55)
Combine and simplify the denominator.
Multiply 25 and 55.
y=±i(2555)
Raise 5 to the power of 1.
y=±i(2555)
Raise 5 to the power of 1.
y=±i(2555)
Use the power rule aman=am+n to combine exponents.
y=±i(2551+1)
y=±i(2552)
Rewrite 52 as 5.
Use axn=axn to rewrite 5 as 512.
y=±i(25(512)2)
Apply the power rule and multiply exponents, (am)n=amn.
y=±i(25512⋅2)
Combine 12 and 2.
y=±i(25522)
Cancel the common factor of 2.
Cancel the common factor.
y=±i(25522)
Divide 1 by 1.
y=±i(255)
y=±i(255)
Evaluate the exponent.
y=±i(255)
y=±i(255)
y=±i(255)
Simplify the numerator.
Combine using the product rule for radicals.
y=±i(2⋅55)
Multiply 2 by 5.
y=±i(105)
y=±i(105)
Combine i and 105.
y=±i105
y=±i105
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
y=i105
Next, use the negative value of the ± to find the second solution.
y=-i105
The complete solution is the result of both the positive and negative portions of the solution.
y=i105,-i105
y=i105,-i105
y=i105,-i105
Solve for y 5y^2+2=0

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