2*x^2-2*x-1000000=0

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Solution for 2*x^2-2*x-1000000=0 equation: 


Simplifying
2x2 + -2x + -1000000 = 0

Reorder the terms:
-1000000 + -2x + 2x2 = 0

Solving
-1000000 + -2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-500000 + -1x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-500000 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-500000 + -1x + x2 = 0

Solving
-500000 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '500000' to each side of the equation.
-500000 + -1x + 500000 + x2 = 0 + 500000

Reorder the terms:
-500000 + 500000 + -1x + x2 = 0 + 500000

Combine like terms: -500000 + 500000 = 0
0 + -1x + x2 = 0 + 500000
-1x + x2 = 0 + 500000

Combine like terms: 0 + 500000 = 500000
-1x + x2 = 500000

The x term is -1x.  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.
-1x + 0.25 + x2 = 500000 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 500000 + 0.25

Combine like terms: 500000 + 0.25 = 500000.25
0.25 + -1x + x2 = 500000.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 500000.25

Calculate the square root of the right side: 707.106957963

Break this problem into two subproblems by setting 
(x + -0.5) equal to 707.106957963 and -707.106957963.


Subproblem 1
x + -0.5 = 707.106957963

Simplifying
x + -0.5 = 707.106957963

Reorder the terms:
-0.5 + x = 707.106957963

Solving
-0.5 + x = 707.106957963

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 = 707.106957963 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 707.106957963 + 0.5
x = 707.106957963 + 0.5

Combine like terms: 707.106957963 + 0.5 = 707.606957963
x = 707.606957963

Simplifying
x = 707.606957963


Subproblem 2
x + -0.5 = -707.106957963

Simplifying
x + -0.5 = -707.106957963

Reorder the terms:
-0.5 + x = -707.106957963

Solving
-0.5 + x = -707.106957963

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 = -707.106957963 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -707.106957963 + 0.5
x = -707.106957963 + 0.5

Combine like terms: -707.106957963 + 0.5 = -706.606957963
x = -706.606957963

Simplifying
x = -706.606957963


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {707.606957963, -706.606957963}
Solution
x = {707.606957963, -706.606957963}

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