4x^2-20x-8400=0

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Solution for 4x^2-20x-8400=0 equation: 


Simplifying
4x2 + -20x + -8400 = 0

Reorder the terms:
-8400 + -20x + 4x2 = 0

Solving
-8400 + -20x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2100 + -5x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2100 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-2100 + -5x + x2 = 0

Solving
-2100 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2100' to each side of the equation.
-2100 + -5x + 2100 + x2 = 0 + 2100

Reorder the terms:
-2100 + 2100 + -5x + x2 = 0 + 2100

Combine like terms: -2100 + 2100 = 0
0 + -5x + x2 = 0 + 2100
-5x + x2 = 0 + 2100

Combine like terms: 0 + 2100 = 2100
-5x + x2 = 2100

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 2100 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 2100 + 6.25

Combine like terms: 2100 + 6.25 = 2106.25
6.25 + -5x + x2 = 2106.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 2106.25

Calculate the square root of the right side: 45.893899377

Break this problem into two subproblems by setting 
(x + -2.5) equal to 45.893899377 and -45.893899377.


Subproblem 1
x + -2.5 = 45.893899377

Simplifying
x + -2.5 = 45.893899377

Reorder the terms:
-2.5 + x = 45.893899377

Solving
-2.5 + x = 45.893899377

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 45.893899377 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 45.893899377 + 2.5
x = 45.893899377 + 2.5

Combine like terms: 45.893899377 + 2.5 = 48.393899377
x = 48.393899377

Simplifying
x = 48.393899377


Subproblem 2
x + -2.5 = -45.893899377

Simplifying
x + -2.5 = -45.893899377

Reorder the terms:
-2.5 + x = -45.893899377

Solving
-2.5 + x = -45.893899377

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -45.893899377 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -45.893899377 + 2.5
x = -45.893899377 + 2.5

Combine like terms: -45.893899377 + 2.5 = -43.393899377
x = -43.393899377

Simplifying
x = -43.393899377


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {48.393899377, -43.393899377}
Solution
x = {48.393899377, -43.393899377}

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