72x^2+18x+3=0

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Solution for 72x^2+18x+3=0 equation: 


Simplifying
72x2 + 18x + 3 = 0

Reorder the terms:
3 + 18x + 72x2 = 0

Solving
3 + 18x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 6x + 24x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + 6x + 24x2)' equal to zero and attempt to solve:

Simplifying
1 + 6x + 24x2 = 0

Solving
1 + 6x + 24x2 = 0

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

Divide each side by '24'.
0.04166666667 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-0.04166666667' to each side of the equation.
0.04166666667 + 0.25x + -0.04166666667 + x2 = 0 + -0.04166666667

Reorder the terms:
0.04166666667 + -0.04166666667 + 0.25x + x2 = 0 + -0.04166666667

Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000
0.00000000000 + 0.25x + x2 = 0 + -0.04166666667
0.25x + x2 = 0 + -0.04166666667

Combine like terms: 0 + -0.04166666667 = -0.04166666667
0.25x + x2 = -0.04166666667

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = -0.04166666667 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = -0.04166666667 + 0.015625

Combine like terms: -0.04166666667 + 0.015625 = -0.02604166667
0.015625 + 0.25x + x2 = -0.02604166667

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = -0.02604166667

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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