3a^2+xa=x^2

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Solution for 3a^2+xa=x^2 equation: 


Simplifying
3a2 + xa = x2

Reorder the terms:
ax + 3a2 = x2

Solving
ax + 3a2 = x2

Solving for variable 'a'.

Combine like terms: x2 + -1x2 = 0
ax + 3a2 + -1x2 = 0

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

Divide each side by '3'.
0.3333333333ax + a2 + -0.3333333333x2 = 0

Move the constant term to the right:

Add '0.3333333333x2' to each side of the equation.
0.3333333333ax + a2 + -0.3333333333x2 + 0.3333333333x2 = 0 + 0.3333333333x2

Combine like terms: -0.3333333333x2 + 0.3333333333x2 = 0.0000000000
0.3333333333ax + a2 + 0.0000000000 = 0 + 0.3333333333x2
0.3333333333ax + a2 = 0 + 0.3333333333x2
Remove the zero:
0.3333333333ax + a2 = 0.3333333333x2

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.
0.3333333333ax + a2 + 0.25x2 = 0.3333333333x2 + 0.25x2

Combine like terms: 0.3333333333x2 + 0.25x2 = 0.5833333333x2
0.3333333333ax + a2 + 0.25x2 = 0.5833333333x2

Factor a perfect square on the left side:
(a + 0.5x)(a + 0.5x) = 0.5833333333x2

Calculate the square root of the right side: 0.763762616x

Break this problem into two subproblems by setting 
(a + 0.5x) equal to 0.763762616x and -0.763762616x.


Subproblem 1
a + 0.5x = 0.763762616x

Simplifying
a + 0.5x = 0.763762616x

Solving
a + 0.5x = 0.763762616x

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.5x' to each side of the equation.
a + 0.5x + -0.5x = 0.763762616x + -0.5x

Combine like terms: 0.5x + -0.5x = 0.0
a + 0.0 = 0.763762616x + -0.5x
a = 0.763762616x + -0.5x

Combine like terms: 0.763762616x + -0.5x = 0.263762616x
a = 0.263762616x

Simplifying
a = 0.263762616x


Subproblem 2
a + 0.5x = -0.763762616x

Simplifying
a + 0.5x = -0.763762616x

Solving
a + 0.5x = -0.763762616x

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.5x' to each side of the equation.
a + 0.5x + -0.5x = -0.763762616x + -0.5x

Combine like terms: 0.5x + -0.5x = 0.0
a + 0.0 = -0.763762616x + -0.5x
a = -0.763762616x + -0.5x

Combine like terms: -0.763762616x + -0.5x = -1.263762616x
a = -1.263762616x

Simplifying
a = -1.263762616x


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.263762616x, -1.263762616x}

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