4x^2+400x-4100=0

Solution for 4x^2+400x-4100=0 equation:

Simplifying
4x2 + 400x + -4100 = 0

Reorder the terms:
-4100 + 400x + 4x2 = 0

Solving
-4100 + 400x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1025 + 100x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1025 + 100x + x2)' equal to zero and attempt to solve:

Simplifying
-1025 + 100x + x2 = 0

Solving
-1025 + 100x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1025' to each side of the equation.
-1025 + 100x + 1025 + x2 = 0 + 1025

Reorder the terms:
-1025 + 1025 + 100x + x2 = 0 + 1025

Combine like terms: -1025 + 1025 = 0
0 + 100x + x2 = 0 + 1025
100x + x2 = 0 + 1025

Combine like terms: 0 + 1025 = 1025
100x + x2 = 1025

The x term is 100x.  Take half its coefficient (50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
100x + 2500 + x2 = 1025 + 2500

Reorder the terms:
2500 + 100x + x2 = 1025 + 2500

Combine like terms: 1025 + 2500 = 3525
2500 + 100x + x2 = 3525

Factor a perfect square on the left side:
(x + 50)(x + 50) = 3525

Calculate the square root of the right side: 59.371710435

Break this problem into two subproblems by setting 
(x + 50) equal to 59.371710435 and -59.371710435.

Subproblem 1
x + 50 = 59.371710435

Simplifying
x + 50 = 59.371710435

Reorder the terms:
50 + x = 59.371710435

Solving
50 + x = 59.371710435

Solving for variable 'x'.

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

Add '-50' to each side of the equation.
50 + -50 + x = 59.371710435 + -50

Combine like terms: 50 + -50 = 0
0 + x = 59.371710435 + -50
x = 59.371710435 + -50

Combine like terms: 59.371710435 + -50 = 9.371710435
x = 9.371710435

Simplifying
x = 9.371710435

Subproblem 2
x + 50 = -59.371710435

Simplifying
x + 50 = -59.371710435

Reorder the terms:
50 + x = -59.371710435

Solving
50 + x = -59.371710435

Solving for variable 'x'.

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

Add '-50' to each side of the equation.
50 + -50 + x = -59.371710435 + -50

Combine like terms: 50 + -50 = 0
0 + x = -59.371710435 + -50
x = -59.371710435 + -50

Combine like terms: -59.371710435 + -50 = -109.371710435
x = -109.371710435

Simplifying
x = -109.371710435

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.371710435, -109.371710435}
Solution
x = {9.371710435, -109.371710435}