0=y^2+2y+7

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Solution for 0=y^2+2y+7 equation: 


Simplifying
0 = y2 + 2y + 7

Reorder the terms:
0 = 7 + 2y + y2

Solving
0 = 7 + 2y + y2

Solving for variable 'y'.

Combine like terms: 0 + -7 = -7
-7 + -2y + -1y2 = 7 + 2y + y2 + -7 + -2y + -1y2

Reorder the terms:
-7 + -2y + -1y2 = 7 + -7 + 2y + -2y + y2 + -1y2

Combine like terms: 7 + -7 = 0
-7 + -2y + -1y2 = 0 + 2y + -2y + y2 + -1y2
-7 + -2y + -1y2 = 2y + -2y + y2 + -1y2

Combine like terms: 2y + -2y = 0
-7 + -2y + -1y2 = 0 + y2 + -1y2
-7 + -2y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-7 + -2y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 2y + y2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + 2y + y2)' equal to zero and attempt to solve:

Simplifying
7 + 2y + y2 = 0

Solving
7 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 2y + -7 + y2 = 0 + -7

Reorder the terms:
7 + -7 + 2y + y2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2y + y2 = 0 + -7
2y + y2 = 0 + -7

Combine like terms: 0 + -7 = -7
2y + y2 = -7

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = -7 + 1

Reorder the terms:
1 + 2y + y2 = -7 + 1

Combine like terms: -7 + 1 = -6
1 + 2y + y2 = -6

Factor a perfect square on the left side:
(y + 1)(y + 1) = -6

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.

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