-1=x^2+2x+3

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Solution for -1=x^2+2x+3 equation:


Simplifying
-1 = x2 + 2x + 3

Reorder the terms:
-1 = 3 + 2x + x2

Solving
-1 = 3 + 2x + x2

Solving for variable 'x'.

Combine like terms: -1 + -3 = -4
-4 + -2x + -1x2 = 3 + 2x + x2 + -3 + -2x + -1x2

Reorder the terms:
-4 + -2x + -1x2 = 3 + -3 + 2x + -2x + x2 + -1x2

Combine like terms: 3 + -3 = 0
-4 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2
-4 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
-4 + -2x + -1x2 = 0 + x2 + -1x2
-4 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + -2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 2x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(4 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
4 + 2x + x2 = 0

Solving
4 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 2x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 2x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 2x + x2 = 0 + -4
2x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
2x + x2 = -4

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

Add '1' to each side of the equation.
2x + 1 + x2 = -4 + 1

Reorder the terms:
1 + 2x + x2 = -4 + 1

Combine like terms: -4 + 1 = -3
1 + 2x + x2 = -3

Factor a perfect square on the left side:
(x + 1)(x + 1) = -3

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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