0=x^2+4x+5

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Solution for 0=x^2+4x+5 equation: 


Simplifying
0 = x2 + 4x + 5

Reorder the terms:
0 = 5 + 4x + x2

Solving
0 = 5 + 4x + x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -4x + -1x2 = 5 + 4x + x2 + -5 + -4x + -1x2

Reorder the terms:
-5 + -4x + -1x2 = 5 + -5 + 4x + -4x + x2 + -1x2

Combine like terms: 5 + -5 = 0
-5 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
-5 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
-5 + -4x + -1x2 = 0 + x2 + -1x2
-5 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + -4x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 4x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 4x + x2 = 0

Solving
5 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 4x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 4x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4x + x2 = 0 + -5
4x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
4x + x2 = -5

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -5 + 4

Reorder the terms:
4 + 4x + x2 = -5 + 4

Combine like terms: -5 + 4 = -1
4 + 4x + x2 = -1

Factor a perfect square on the left side:
(x + 2)(x + 2) = -1

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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