a*a+0.95477*a=0.02618

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Solution for a*a+0.95477*a=0.02618 equation: 


Simplifying
a * a + 0.95477a = 0.02618

Multiply a * a
a2 + 0.95477a = 0.02618

Reorder the terms:
0.95477a + a2 = 0.02618

Solving
0.95477a + a2 = 0.02618

Solving for variable 'a'.

Reorder the terms:
-0.02618 + 0.95477a + a2 = 0.02618 + -0.02618

Combine like terms: 0.02618 + -0.02618 = 0.00000
-0.02618 + 0.95477a + a2 = 0.00000

Begin completing the square.

Move the constant term to the right:

Add '0.02618' to each side of the equation.
-0.02618 + 0.95477a + 0.02618 + a2 = 0.00000 + 0.02618

Reorder the terms:
-0.02618 + 0.02618 + 0.95477a + a2 = 0.00000 + 0.02618

Combine like terms: -0.02618 + 0.02618 = 0.00000
0.00000 + 0.95477a + a2 = 0.00000 + 0.02618
0.95477a + a2 = 0.00000 + 0.02618

Combine like terms: 0.00000 + 0.02618 = 0.02618
0.95477a + a2 = 0.02618

The a term is 0.95477a.  Take half its coefficient (0.477385).
Square it (0.2278964382) and add it to both sides.

Add '0.2278964382' to each side of the equation.
0.95477a + 0.2278964382 + a2 = 0.02618 + 0.2278964382

Reorder the terms:
0.2278964382 + 0.95477a + a2 = 0.02618 + 0.2278964382

Combine like terms: 0.02618 + 0.2278964382 = 0.2540764382
0.2278964382 + 0.95477a + a2 = 0.2540764382

Factor a perfect square on the left side:
(a + 0.477385)(a + 0.477385) = 0.2540764382

Calculate the square root of the right side: 0.504059955

Break this problem into two subproblems by setting 
(a + 0.477385) equal to 0.504059955 and -0.504059955.


Subproblem 1
a + 0.477385 = 0.504059955

Simplifying
a + 0.477385 = 0.504059955

Reorder the terms:
0.477385 + a = 0.504059955

Solving
0.477385 + a = 0.504059955

Solving for variable 'a'.

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

Add '-0.477385' to each side of the equation.
0.477385 + -0.477385 + a = 0.504059955 + -0.477385

Combine like terms: 0.477385 + -0.477385 = 0.000000
0.000000 + a = 0.504059955 + -0.477385
a = 0.504059955 + -0.477385

Combine like terms: 0.504059955 + -0.477385 = 0.026674955
a = 0.026674955

Simplifying
a = 0.026674955


Subproblem 2
a + 0.477385 = -0.504059955

Simplifying
a + 0.477385 = -0.504059955

Reorder the terms:
0.477385 + a = -0.504059955

Solving
0.477385 + a = -0.504059955

Solving for variable 'a'.

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

Add '-0.477385' to each side of the equation.
0.477385 + -0.477385 + a = -0.504059955 + -0.477385

Combine like terms: 0.477385 + -0.477385 = 0.000000
0.000000 + a = -0.504059955 + -0.477385
a = -0.504059955 + -0.477385

Combine like terms: -0.504059955 + -0.477385 = -0.981444955
a = -0.981444955

Simplifying
a = -0.981444955


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.026674955, -0.981444955}

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