-y^2=y+42

Solution for -y^2=y+42 equation:

Simplifying
-1y2 = y + 42

Reorder the terms:
-1y2 = 42 + y

Solving
-1y2 = 42 + y

Solving for variable 'y'.

Reorder the terms:
-42 + -1y + -1y2 = 42 + y + -42 + -1y

Reorder the terms:
-42 + -1y + -1y2 = 42 + -42 + y + -1y

Combine like terms: 42 + -42 = 0
-42 + -1y + -1y2 = 0 + y + -1y
-42 + -1y + -1y2 = y + -1y

Combine like terms: y + -1y = 0
-42 + -1y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(42 + y + y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(42 + y + y2)' equal to zero and attempt to solve:

Simplifying
42 + y + y2 = 0

Solving
42 + y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + y + -42 + y2 = 0 + -42

Reorder the terms:
42 + -42 + y + y2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + y + y2 = 0 + -42
y + y2 = 0 + -42

Combine like terms: 0 + -42 = -42
y + y2 = -42

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
y + 0.25 + y2 = -42 + 0.25

Reorder the terms:
0.25 + y + y2 = -42 + 0.25

Combine like terms: -42 + 0.25 = -41.75
0.25 + y + y2 = -41.75

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = -41.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.