a^2+a-200=0

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Solution for a^2+a-200=0 equation:


Simplifying
a2 + a + -200 = 0

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

Solving
-200 + a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
a + 0.25 + a2 = 200 + 0.25

Reorder the terms:
0.25 + a + a2 = 200 + 0.25

Combine like terms: 200 + 0.25 = 200.25
0.25 + a + a2 = 200.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 200.25

Calculate the square root of the right side: 14.150971698

Break this problem into two subproblems by setting 
(a + 0.5) equal to 14.150971698 and -14.150971698.


Subproblem 1
a + 0.5 = 14.150971698

Simplifying
a + 0.5 = 14.150971698

Reorder the terms:
0.5 + a = 14.150971698

Solving
0.5 + a = 14.150971698

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = 14.150971698 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = 14.150971698 + -0.5
a = 14.150971698 + -0.5

Combine like terms: 14.150971698 + -0.5 = 13.650971698
a = 13.650971698

Simplifying
a = 13.650971698


Subproblem 2
a + 0.5 = -14.150971698

Simplifying
a + 0.5 = -14.150971698

Reorder the terms:
0.5 + a = -14.150971698

Solving
0.5 + a = -14.150971698

Solving for variable 'a'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + a = -14.150971698 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + a = -14.150971698 + -0.5
a = -14.150971698 + -0.5

Combine like terms: -14.150971698 + -0.5 = -14.650971698
a = -14.650971698

Simplifying
a = -14.650971698


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {13.650971698, -14.650971698}

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