a*(a+0.954768)=0.026197

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Solution for a*(a+0.954768)=0.026197 equation: 


Simplifying
a(a + 0.954768) = 0.026197

Reorder the terms:
a(0.954768 + a) = 0.026197
(0.954768 * a + a * a) = 0.026197
(0.954768a + a2) = 0.026197

Solving
0.954768a + a2 = 0.026197

Solving for variable 'a'.

Reorder the terms:
-0.026197 + 0.954768a + a2 = 0.026197 + -0.026197

Combine like terms: 0.026197 + -0.026197 = 0.000000
-0.026197 + 0.954768a + a2 = 0.000000

Begin completing the square.

Move the constant term to the right:

Add '0.026197' to each side of the equation.
-0.026197 + 0.954768a + 0.026197 + a2 = 0.000000 + 0.026197

Reorder the terms:
-0.026197 + 0.026197 + 0.954768a + a2 = 0.000000 + 0.026197

Combine like terms: -0.026197 + 0.026197 = 0.000000
0.000000 + 0.954768a + a2 = 0.000000 + 0.026197
0.954768a + a2 = 0.000000 + 0.026197

Combine like terms: 0.000000 + 0.026197 = 0.026197
0.954768a + a2 = 0.026197

The a term is 0.954768a.  Take half its coefficient (0.477384).
Square it (0.2278954835) and add it to both sides.

Add '0.2278954835' to each side of the equation.
0.954768a + 0.2278954835 + a2 = 0.026197 + 0.2278954835

Reorder the terms:
0.2278954835 + 0.954768a + a2 = 0.026197 + 0.2278954835

Combine like terms: 0.026197 + 0.2278954835 = 0.2540924835
0.2278954835 + 0.954768a + a2 = 0.2540924835

Factor a perfect square on the left side:
(a + 0.477384)(a + 0.477384) = 0.2540924835

Calculate the square root of the right side: 0.504075871

Break this problem into two subproblems by setting 
(a + 0.477384) equal to 0.504075871 and -0.504075871.


Subproblem 1
a + 0.477384 = 0.504075871

Simplifying
a + 0.477384 = 0.504075871

Reorder the terms:
0.477384 + a = 0.504075871

Solving
0.477384 + a = 0.504075871

Solving for variable 'a'.

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

Add '-0.477384' to each side of the equation.
0.477384 + -0.477384 + a = 0.504075871 + -0.477384

Combine like terms: 0.477384 + -0.477384 = 0.000000
0.000000 + a = 0.504075871 + -0.477384
a = 0.504075871 + -0.477384

Combine like terms: 0.504075871 + -0.477384 = 0.026691871
a = 0.026691871

Simplifying
a = 0.026691871


Subproblem 2
a + 0.477384 = -0.504075871

Simplifying
a + 0.477384 = -0.504075871

Reorder the terms:
0.477384 + a = -0.504075871

Solving
0.477384 + a = -0.504075871

Solving for variable 'a'.

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

Add '-0.477384' to each side of the equation.
0.477384 + -0.477384 + a = -0.504075871 + -0.477384

Combine like terms: 0.477384 + -0.477384 = 0.000000
0.000000 + a = -0.504075871 + -0.477384
a = -0.504075871 + -0.477384

Combine like terms: -0.504075871 + -0.477384 = -0.981459871
a = -0.981459871

Simplifying
a = -0.981459871


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.026691871, -0.981459871}

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