6y2=-7-2

Subtract 2 from -7.

6y2=-9

Divide each term in 6y2=-9 by 6.

6y26=-96

Cancel the common factor of 6.

Cancel the common factor.

6y26=-96

Divide y2 by 1.

y2=-96

y2=-96

Simplify -96.

Cancel the common factor of -9 and 6.

Factor 3 out of -9.

y2=3(-3)6

Cancel the common factors.

Factor 3 out of 6.

y2=3⋅-33⋅2

Cancel the common factor.

y2=3⋅-33⋅2

Rewrite the expression.

y2=-32

y2=-32

y2=-32

Move the negative in front of the fraction.

y2=-32

y2=-32

y2=-32

Take the square root of both sides of the equation to eliminate the exponent on the left side.

y=±-32

Simplify the right side of the equation.

Rewrite -1 as i2.

y=±i2(32)

Pull terms out from under the radical.

y=±i32

Rewrite 32 as 32.

y=±i(32)

Multiply 32 by 22.

y=±i(32⋅22)

Combine and simplify the denominator.

Multiply 32 and 22.

y=±i(3222)

Raise 2 to the power of 1.

y=±i(3222)

Raise 2 to the power of 1.

y=±i(3222)

Use the power rule aman=am+n to combine exponents.

y=±i(3221+1)

Add 1 and 1.

y=±i(3222)

Rewrite 22 as 2.

Use axn=axn to rewrite 2 as 212.

y=±i(32(212)2)

Apply the power rule and multiply exponents, (am)n=amn.

y=±i(32212⋅2)

Combine 12 and 2.

y=±i(32222)

Cancel the common factor of 2.

Cancel the common factor.

y=±i(32222)

Divide 1 by 1.

y=±i(322)

y=±i(322)

Evaluate the exponent.

y=±i(322)

y=±i(322)

y=±i(322)

Simplify the numerator.

Combine using the product rule for radicals.

y=±i(3⋅22)

Multiply 3 by 2.

y=±i(62)

y=±i(62)

Combine i and 62.

y=±i62

y=±i62

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=i62

Next, use the negative value of the ± to find the second solution.

y=-i62

The complete solution is the result of both the positive and negative portions of the solution.

y=i62,-i62

y=i62,-i62

y=i62,-i62

Solve for y 6y^2=-7-2