x^2+5=-x

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Solution for x^2+5=-x equation:


Simplifying
x2 + 5 = -1x

Reorder the terms:
5 + x2 = -1x

Solving
5 + x2 = -1x

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is x.  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.
x + 0.25 + x2 = -5 + 0.25

Reorder the terms:
0.25 + x + x2 = -5 + 0.25

Combine like terms: -5 + 0.25 = -4.75
0.25 + x + x2 = -4.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -4.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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