12X^2+56X+84=0

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Solution for 12X^2+56X+84=0 equation: 


Simplifying
12X2 + 56X + 84 = 0

Reorder the terms:
84 + 56X + 12X2 = 0

Solving
84 + 56X + 12X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '4'.
4(21 + 14X + 3X2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(21 + 14X + 3X2)' equal to zero and attempt to solve:

Simplifying
21 + 14X + 3X2 = 0

Solving
21 + 14X + 3X2 = 0

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

Divide each side by '3'.
7 + 4.666666667X + X2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 4.666666667X + -7 + X2 = 0 + -7

Reorder the terms:
7 + -7 + 4.666666667X + X2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4.666666667X + X2 = 0 + -7
4.666666667X + X2 = 0 + -7

Combine like terms: 0 + -7 = -7
4.666666667X + X2 = -7

The X term is 4.666666667X.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667X + 5.444444448 + X2 = -7 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667X + X2 = -7 + 5.444444448

Combine like terms: -7 + 5.444444448 = -1.555555552
5.444444448 + 4.666666667X + X2 = -1.555555552

Factor a perfect square on the left side:
(X + 2.333333334)(X + 2.333333334) = -1.555555552

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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