16x^2+68x+108=0

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Solution for 16x^2+68x+108=0 equation: 


Simplifying
16x2 + 68x + 108 = 0

Reorder the terms:
108 + 68x + 16x2 = 0

Solving
108 + 68x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(27 + 17x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(27 + 17x + 4x2)' equal to zero and attempt to solve:

Simplifying
27 + 17x + 4x2 = 0

Solving
27 + 17x + 4x2 = 0

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

Divide each side by '4'.
6.75 + 4.25x + x2 = 0

Move the constant term to the right:

Add '-6.75' to each side of the equation.
6.75 + 4.25x + -6.75 + x2 = 0 + -6.75

Reorder the terms:
6.75 + -6.75 + 4.25x + x2 = 0 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + 4.25x + x2 = 0 + -6.75
4.25x + x2 = 0 + -6.75

Combine like terms: 0 + -6.75 = -6.75
4.25x + x2 = -6.75

The x term is 4.25x.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25x + 4.515625 + x2 = -6.75 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = -6.75 + 4.515625

Combine like terms: -6.75 + 4.515625 = -2.234375
4.515625 + 4.25x + x2 = -2.234375

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = -2.234375

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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