a(253.98+184a)-678-7-a+74(122)(37)=3

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Solution for a(253.98+184a)-678-7-a+74(122)(37)=3 equation:


Simplifying
a(253.98 + 184a) + -678 + -7 + -1a + 74(122)(37) = 3
(253.98 * a + 184a * a) + -678 + -7 + -1a + 74(122)(37) = 3
(253.98a + 184a2) + -678 + -7 + -1a + 74(122)(37) = 3

Multiply 74 * 122
253.98a + 184a2 + -678 + -7 + -1a + 9028 * 37 = 3

Multiply 9028 * 37
253.98a + 184a2 + -678 + -7 + -1a + 334036 = 3

Reorder the terms:
-678 + -7 + 334036 + 253.98a + -1a + 184a2 = 3

Combine like terms: -678 + -7 = -685
-685 + 334036 + 253.98a + -1a + 184a2 = 3

Combine like terms: -685 + 334036 = 333351
333351 + 253.98a + -1a + 184a2 = 3

Combine like terms: 253.98a + -1a = 252.98a
333351 + 252.98a + 184a2 = 3

Solving
333351 + 252.98a + 184a2 = 3

Solving for variable 'a'.

Reorder the terms:
333351 + -3 + 252.98a + 184a2 = 3 + -3

Combine like terms: 333351 + -3 = 333348
333348 + 252.98a + 184a2 = 3 + -3

Combine like terms: 3 + -3 = 0
333348 + 252.98a + 184a2 = 0

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

Divide each side by '184'.
1811.673913 + 1.374891304a + a2 = 0

Move the constant term to the right:

Add '-1811.673913' to each side of the equation.
1811.673913 + 1.374891304a + -1811.673913 + a2 = 0 + -1811.673913

Reorder the terms:
1811.673913 + -1811.673913 + 1.374891304a + a2 = 0 + -1811.673913

Combine like terms: 1811.673913 + -1811.673913 = 0.000000
0.000000 + 1.374891304a + a2 = 0 + -1811.673913
1.374891304a + a2 = 0 + -1811.673913

Combine like terms: 0 + -1811.673913 = -1811.673913
1.374891304a + a2 = -1811.673913

The a term is 1.374891304a.  Take half its coefficient (0.687445652).
Square it (0.4725815245) and add it to both sides.

Add '0.4725815245' to each side of the equation.
1.374891304a + 0.4725815245 + a2 = -1811.673913 + 0.4725815245

Reorder the terms:
0.4725815245 + 1.374891304a + a2 = -1811.673913 + 0.4725815245

Combine like terms: -1811.673913 + 0.4725815245 = -1811.2013314755
0.4725815245 + 1.374891304a + a2 = -1811.2013314755

Factor a perfect square on the left side:
(a + 0.687445652)(a + 0.687445652) = -1811.2013314755

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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