x^2+x-202=0

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Solution for x^2+x-202=0 equation: 


Simplifying
x2 + x + -202 = 0

Reorder the terms:
-202 + x + x2 = 0

Solving
-202 + x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '202' to each side of the equation.
-202 + x + 202 + x2 = 0 + 202

Reorder the terms:
-202 + 202 + x + x2 = 0 + 202

Combine like terms: -202 + 202 = 0
0 + x + x2 = 0 + 202
x + x2 = 0 + 202

Combine like terms: 0 + 202 = 202
x + x2 = 202

The x term is x.  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.
x + 0.25 + x2 = 202 + 0.25

Reorder the terms:
0.25 + x + x2 = 202 + 0.25

Combine like terms: 202 + 0.25 = 202.25
0.25 + x + x2 = 202.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 202.25

Calculate the square root of the right side: 14.221462653

Break this problem into two subproblems by setting 
(x + 0.5) equal to 14.221462653 and -14.221462653.


Subproblem 1
x + 0.5 = 14.221462653

Simplifying
x + 0.5 = 14.221462653

Reorder the terms:
0.5 + x = 14.221462653

Solving
0.5 + x = 14.221462653

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 14.221462653 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 14.221462653 + -0.5
x = 14.221462653 + -0.5

Combine like terms: 14.221462653 + -0.5 = 13.721462653
x = 13.721462653

Simplifying
x = 13.721462653


Subproblem 2
x + 0.5 = -14.221462653

Simplifying
x + 0.5 = -14.221462653

Reorder the terms:
0.5 + x = -14.221462653

Solving
0.5 + x = -14.221462653

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -14.221462653 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -14.221462653 + -0.5
x = -14.221462653 + -0.5

Combine like terms: -14.221462653 + -0.5 = -14.721462653
x = -14.721462653

Simplifying
x = -14.721462653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.721462653, -14.721462653}

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