|c2-3|=5

Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.

c2-3=±5

Set up the positive portion of the ± solution.

c2-3=5

Move all terms not containing c to the right side of the equation.

Add 3 to both sides of the equation.

c2=5+3

Add 5 and 3.

c2=8

c2=8

Multiply both sides of the equation by 2.

2⋅c2=2⋅8

Simplify both sides of the equation.

Cancel the common factor of 2.

Cancel the common factor.

2⋅c2=2⋅8

Rewrite the expression.

c=2⋅8

c=2⋅8

Multiply 2 by 8.

c=16

c=16

c=16

Set up the negative portion of the ± solution.

c2-3=-5

Move all terms not containing c to the right side of the equation.

Add 3 to both sides of the equation.

c2=-5+3

Add -5 and 3.

c2=-2

c2=-2

Multiply both sides of the equation by 2.

2⋅c2=2⋅-2

Simplify both sides of the equation.

Cancel the common factor of 2.

Cancel the common factor.

2⋅c2=2⋅-2

Rewrite the expression.

c=2⋅-2

c=2⋅-2

Multiply 2 by -2.

c=-4

c=-4

c=-4

The solution to the equation includes both the positive and negative portions of the solution.

c=16,-4

Evaluate |c/2-3|=5