4x^2+8x+31=0

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Solution for 4x^2+8x+31=0 equation:


Simplifying
4x2 + 8x + 31 = 0

Reorder the terms:
31 + 8x + 4x2 = 0

Solving
31 + 8x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
7.75 + 2x + x2 = 0

Move the constant term to the right:

Add '-7.75' to each side of the equation.
7.75 + 2x + -7.75 + x2 = 0 + -7.75

Reorder the terms:
7.75 + -7.75 + 2x + x2 = 0 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + 2x + x2 = 0 + -7.75
2x + x2 = 0 + -7.75

Combine like terms: 0 + -7.75 = -7.75
2x + x2 = -7.75

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 = -7.75 + 1

Reorder the terms:
1 + 2x + x2 = -7.75 + 1

Combine like terms: -7.75 + 1 = -6.75
1 + 2x + x2 = -6.75

Factor a perfect square on the left side:
(x + 1)(x + 1) = -6.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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