4x^2+16x+31=0

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Solution for 4x^2+16x+31=0 equation:


Simplifying
4x2 + 16x + 31 = 0

Reorder the terms:
31 + 16x + 4x2 = 0

Solving
31 + 16x + 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 + 4x + x2 = 0

Move the constant term to the right:

Add '-7.75' to each side of the equation.
7.75 + 4x + -7.75 + x2 = 0 + -7.75

Reorder the terms:
7.75 + -7.75 + 4x + x2 = 0 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + 4x + x2 = 0 + -7.75
4x + x2 = 0 + -7.75

Combine like terms: 0 + -7.75 = -7.75
4x + x2 = -7.75

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 = -7.75 + 4

Reorder the terms:
4 + 4x + x2 = -7.75 + 4

Combine like terms: -7.75 + 4 = -3.75
4 + 4x + x2 = -3.75

Factor a perfect square on the left side:
(x + 2)(x + 2) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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