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

6y2=-7-2
Subtract 2 from -7.
6y2=-9
Divide each term by 6 and simplify.
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
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(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)
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

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