3x^2+4ax+4a^2=0

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Solution for 3x^2+4ax+4a^2=0 equation:


Simplifying
3x2 + 4ax + 4a2 = 0

Reorder the terms:
4ax + 4a2 + 3x2 = 0

Solving
4ax + 4a2 + 3x2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
ax + a2 + 0.75x2 = 0

Move the constant term to the right:

Add '-0.75x2' to each side of the equation.
ax + a2 + 0.75x2 + -0.75x2 = 0 + -0.75x2

Combine like terms: 0.75x2 + -0.75x2 = 0.00
ax + a2 + 0.00 = 0 + -0.75x2
ax + a2 = 0 + -0.75x2
Remove the zero:
ax + a2 = -0.75x2

The a term is ax.  Take half its coefficient (0.5x).
Square it (0.25x2) and add it to both sides.

Add '0.25x2' to each side of the equation.
x2 + a2 + 0.25x2 = -0.75x2 + 0.25x2

Reorder the terms:
a2 + x2 + 0.25x2 = -0.75x2 + 0.25x2

Combine like terms: x2 + 0.25x2 = 1.25x2
a2 + 1.25x2 = -0.75x2 + 0.25x2

Combine like terms: -0.75x2 + 0.25x2 = -0.5x2
a2 + 1.25x2 = -0.5x2

Factor a perfect square on the left side:
(a + 0.5x)(a + 0.5x) = -0.5x2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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