4x^2+800x-5781.6=0

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Solution for 4x^2+800x-5781.6=0 equation: 


Simplifying
4x2 + 800x + -5781.6 = 0

Reorder the terms:
-5781.6 + 800x + 4x2 = 0

Solving
-5781.6 + 800x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-1445.4 + 200x + x2 = 0

Move the constant term to the right:

Add '1445.4' to each side of the equation.
-1445.4 + 200x + 1445.4 + x2 = 0 + 1445.4

Reorder the terms:
-1445.4 + 1445.4 + 200x + x2 = 0 + 1445.4

Combine like terms: -1445.4 + 1445.4 = 0.0
0.0 + 200x + x2 = 0 + 1445.4
200x + x2 = 0 + 1445.4

Combine like terms: 0 + 1445.4 = 1445.4
200x + x2 = 1445.4

The x term is 200x.  Take half its coefficient (100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
200x + 10000 + x2 = 1445.4 + 10000

Reorder the terms:
10000 + 200x + x2 = 1445.4 + 10000

Combine like terms: 1445.4 + 10000 = 11445.4
10000 + 200x + x2 = 11445.4

Factor a perfect square on the left side:
(x + 100)(x + 100) = 11445.4

Calculate the square root of the right side: 106.983176247

Break this problem into two subproblems by setting 
(x + 100) equal to 106.983176247 and -106.983176247.


Subproblem 1
x + 100 = 106.983176247

Simplifying
x + 100 = 106.983176247

Reorder the terms:
100 + x = 106.983176247

Solving
100 + x = 106.983176247

Solving for variable 'x'.

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

Add '-100' to each side of the equation.
100 + -100 + x = 106.983176247 + -100

Combine like terms: 100 + -100 = 0
0 + x = 106.983176247 + -100
x = 106.983176247 + -100

Combine like terms: 106.983176247 + -100 = 6.983176247
x = 6.983176247

Simplifying
x = 6.983176247


Subproblem 2
x + 100 = -106.983176247

Simplifying
x + 100 = -106.983176247

Reorder the terms:
100 + x = -106.983176247

Solving
100 + x = -106.983176247

Solving for variable 'x'.

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

Add '-100' to each side of the equation.
100 + -100 + x = -106.983176247 + -100

Combine like terms: 100 + -100 = 0
0 + x = -106.983176247 + -100
x = -106.983176247 + -100

Combine like terms: -106.983176247 + -100 = -206.983176247
x = -206.983176247

Simplifying
x = -206.983176247


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.983176247, -206.983176247}

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