48400=(2x+2)(x)

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Solution for 48400=(2x+2)(x) equation: 


Simplifying
48400 = (2x + 2)(x)

Reorder the terms:
48400 = (2 + 2x)(x)

Reorder the terms for easier multiplication:
48400 = x(2 + 2x)
48400 = (2 * x + 2x * x)
48400 = (2x + 2x2)

Solving
48400 = 2x + 2x2

Solving for variable 'x'.

Reorder the terms:
48400 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2

Combine like terms: 2x + -2x = 0
48400 + -2x + -2x2 = 0 + 2x2 + -2x2
48400 + -2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
48400 + -2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24200 + -1x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(24200 + -1x + -1x2)' equal to zero and attempt to solve:

Simplifying
24200 + -1x + -1x2 = 0

Solving
24200 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-24200 + x + x2 = 0

Move the constant term to the right:

Add '24200' to each side of the equation.
-24200 + x + 24200 + x2 = 0 + 24200

Reorder the terms:
-24200 + 24200 + x + x2 = 0 + 24200

Combine like terms: -24200 + 24200 = 0
0 + x + x2 = 0 + 24200
x + x2 = 0 + 24200

Combine like terms: 0 + 24200 = 24200
x + x2 = 24200

The x term is x.  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.
 + 0.25 + x2 = 24200 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 24200 + 0.25

Combine like terms: 24200 + 0.25 = 24200.25
1.25 + x2 = 24200.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 24200.25

Calculate the square root of the right side: 155.564295389

Break this problem into two subproblems by setting 
(x + 0.5) equal to 155.564295389 and -155.564295389.


Subproblem 1
x + 0.5 = 155.564295389

Simplifying
x + 0.5 = 155.564295389

Reorder the terms:
0.5 + x = 155.564295389

Solving
0.5 + x = 155.564295389

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 = 155.564295389 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 155.564295389 + -0.5
x = 155.564295389 + -0.5

Combine like terms: 155.564295389 + -0.5 = 155.064295389
x = 155.064295389

Simplifying
x = 155.064295389


Subproblem 2
x + 0.5 = -155.564295389

Simplifying
x + 0.5 = -155.564295389

Reorder the terms:
0.5 + x = -155.564295389

Solving
0.5 + x = -155.564295389

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 = -155.564295389 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -155.564295389 + -0.5
x = -155.564295389 + -0.5

Combine like terms: -155.564295389 + -0.5 = -156.064295389
x = -156.064295389

Simplifying
x = -156.064295389


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {155.064295389, -156.064295389}
Solution
x = {155.064295389, -156.064295389}

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