x^2-3x-203=0

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Solution for x^2-3x-203=0 equation: 


Simplifying
x2 + -3x + -203 = 0

Reorder the terms:
-203 + -3x + x2 = 0

Solving
-203 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '203' to each side of the equation.
-203 + -3x + 203 + x2 = 0 + 203

Reorder the terms:
-203 + 203 + -3x + x2 = 0 + 203

Combine like terms: -203 + 203 = 0
0 + -3x + x2 = 0 + 203
-3x + x2 = 0 + 203

Combine like terms: 0 + 203 = 203
-3x + x2 = 203

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 203 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 203 + 2.25

Combine like terms: 203 + 2.25 = 205.25
2.25 + -3x + x2 = 205.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 205.25

Calculate the square root of the right side: 14.326548782

Break this problem into two subproblems by setting 
(x + -1.5) equal to 14.326548782 and -14.326548782.


Subproblem 1
x + -1.5 = 14.326548782

Simplifying
x + -1.5 = 14.326548782

Reorder the terms:
-1.5 + x = 14.326548782

Solving
-1.5 + x = 14.326548782

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 14.326548782 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 14.326548782 + 1.5
x = 14.326548782 + 1.5

Combine like terms: 14.326548782 + 1.5 = 15.826548782
x = 15.826548782

Simplifying
x = 15.826548782


Subproblem 2
x + -1.5 = -14.326548782

Simplifying
x + -1.5 = -14.326548782

Reorder the terms:
-1.5 + x = -14.326548782

Solving
-1.5 + x = -14.326548782

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -14.326548782 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -14.326548782 + 1.5
x = -14.326548782 + 1.5

Combine like terms: -14.326548782 + 1.5 = -12.826548782
x = -12.826548782

Simplifying
x = -12.826548782


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.826548782, -12.826548782}

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