5y2+2=0

Subtract 2 from both sides of the equation.

5y2=-2

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

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)

Add 1 and 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