10x^2+40x-2000=0

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Solution for 10x^2+40x-2000=0 equation: 


Simplifying
10x2 + 40x + -2000 = 0

Reorder the terms:
-2000 + 40x + 10x2 = 0

Solving
-2000 + 40x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-200 + 4x + x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-200 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-200 + 4x + x2 = 0

Solving
-200 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + 4x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + 4x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + 4x + x2 = 0 + 200
4x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
4x + x2 = 200

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 200 + 4

Reorder the terms:
4 + 4x + x2 = 200 + 4

Combine like terms: 200 + 4 = 204
4 + 4x + x2 = 204

Factor a perfect square on the left side:
(x + 2)(x + 2) = 204

Calculate the square root of the right side: 14.282856857

Break this problem into two subproblems by setting 
(x + 2) equal to 14.282856857 and -14.282856857.


Subproblem 1
x + 2 = 14.282856857

Simplifying
x + 2 = 14.282856857

Reorder the terms:
2 + x = 14.282856857

Solving
2 + x = 14.282856857

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 14.282856857 + -2

Combine like terms: 2 + -2 = 0
0 + x = 14.282856857 + -2
x = 14.282856857 + -2

Combine like terms: 14.282856857 + -2 = 12.282856857
x = 12.282856857

Simplifying
x = 12.282856857


Subproblem 2
x + 2 = -14.282856857

Simplifying
x + 2 = -14.282856857

Reorder the terms:
2 + x = -14.282856857

Solving
2 + x = -14.282856857

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -14.282856857 + -2

Combine like terms: 2 + -2 = 0
0 + x = -14.282856857 + -2
x = -14.282856857 + -2

Combine like terms: -14.282856857 + -2 = -16.282856857
x = -16.282856857

Simplifying
x = -16.282856857


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.282856857, -16.282856857}
Solution
x = {12.282856857, -16.282856857}

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