4a^2+800a+4200=0

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Solution for 4a^2+800a+4200=0 equation: 


Simplifying
4a2 + 800a + 4200 = 0

Reorder the terms:
4200 + 800a + 4a2 = 0

Solving
4200 + 800a + 4a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1050 + 200a + a2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1050 + 200a + a2)' equal to zero and attempt to solve:

Simplifying
1050 + 200a + a2 = 0

Solving
1050 + 200a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1050' to each side of the equation.
1050 + 200a + -1050 + a2 = 0 + -1050

Reorder the terms:
1050 + -1050 + 200a + a2 = 0 + -1050

Combine like terms: 1050 + -1050 = 0
0 + 200a + a2 = 0 + -1050
200a + a2 = 0 + -1050

Combine like terms: 0 + -1050 = -1050
200a + a2 = -1050

The a term is 200a.  Take half its coefficient (100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
200a + 10000 + a2 = -1050 + 10000

Reorder the terms:
10000 + 200a + a2 = -1050 + 10000

Combine like terms: -1050 + 10000 = 8950
10000 + 200a + a2 = 8950

Factor a perfect square on the left side:
(a + 100)(a + 100) = 8950

Calculate the square root of the right side: 94.604439642

Break this problem into two subproblems by setting 
(a + 100) equal to 94.604439642 and -94.604439642.


Subproblem 1
a + 100 = 94.604439642

Simplifying
a + 100 = 94.604439642

Reorder the terms:
100 + a = 94.604439642

Solving
100 + a = 94.604439642

Solving for variable 'a'.

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

Add '-100' to each side of the equation.
100 + -100 + a = 94.604439642 + -100

Combine like terms: 100 + -100 = 0
0 + a = 94.604439642 + -100
a = 94.604439642 + -100

Combine like terms: 94.604439642 + -100 = -5.395560358
a = -5.395560358

Simplifying
a = -5.395560358


Subproblem 2
a + 100 = -94.604439642

Simplifying
a + 100 = -94.604439642

Reorder the terms:
100 + a = -94.604439642

Solving
100 + a = -94.604439642

Solving for variable 'a'.

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

Add '-100' to each side of the equation.
100 + -100 + a = -94.604439642 + -100

Combine like terms: 100 + -100 = 0
0 + a = -94.604439642 + -100
a = -94.604439642 + -100

Combine like terms: -94.604439642 + -100 = -194.604439642
a = -194.604439642

Simplifying
a = -194.604439642


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-5.395560358, -194.604439642}
Solution
a = {-5.395560358, -194.604439642}

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