4x^2+21x+67=0

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Solution for 4x^2+21x+67=0 equation:


Simplifying
4x2 + 21x + 67 = 0

Reorder the terms:
67 + 21x + 4x2 = 0

Solving
67 + 21x + 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'.
16.75 + 5.25x + x2 = 0

Move the constant term to the right:

Add '-16.75' to each side of the equation.
16.75 + 5.25x + -16.75 + x2 = 0 + -16.75

Reorder the terms:
16.75 + -16.75 + 5.25x + x2 = 0 + -16.75

Combine like terms: 16.75 + -16.75 = 0.00
0.00 + 5.25x + x2 = 0 + -16.75
5.25x + x2 = 0 + -16.75

Combine like terms: 0 + -16.75 = -16.75
5.25x + x2 = -16.75

The x term is 5.25x.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25x + 6.890625 + x2 = -16.75 + 6.890625

Reorder the terms:
6.890625 + 5.25x + x2 = -16.75 + 6.890625

Combine like terms: -16.75 + 6.890625 = -9.859375
6.890625 + 5.25x + x2 = -9.859375

Factor a perfect square on the left side:
(x + 2.625)(x + 2.625) = -9.859375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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