2x^2+200x-2400=0

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Solution for 2x^2+200x-2400=0 equation: 


Simplifying
2x2 + 200x + -2400 = 0

Reorder the terms:
-2400 + 200x + 2x2 = 0

Solving
-2400 + 200x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1200 + 100x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1200 + 100x + x2)' equal to zero and attempt to solve:

Simplifying
-1200 + 100x + x2 = 0

Solving
-1200 + 100x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1200' to each side of the equation.
-1200 + 100x + 1200 + x2 = 0 + 1200

Reorder the terms:
-1200 + 1200 + 100x + x2 = 0 + 1200

Combine like terms: -1200 + 1200 = 0
0 + 100x + x2 = 0 + 1200
100x + x2 = 0 + 1200

Combine like terms: 0 + 1200 = 1200
100x + x2 = 1200

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 = 1200 + 2500

Reorder the terms:
2500 + 100x + x2 = 1200 + 2500

Combine like terms: 1200 + 2500 = 3700
2500 + 100x + x2 = 3700

Factor a perfect square on the left side:
(x + 50)(x + 50) = 3700

Calculate the square root of the right side: 60.827625303

Break this problem into two subproblems by setting 
(x + 50) equal to 60.827625303 and -60.827625303.


Subproblem 1
x + 50 = 60.827625303

Simplifying
x + 50 = 60.827625303

Reorder the terms:
50 + x = 60.827625303

Solving
50 + x = 60.827625303

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 = 60.827625303 + -50

Combine like terms: 50 + -50 = 0
0 + x = 60.827625303 + -50
x = 60.827625303 + -50

Combine like terms: 60.827625303 + -50 = 10.827625303
x = 10.827625303

Simplifying
x = 10.827625303


Subproblem 2
x + 50 = -60.827625303

Simplifying
x + 50 = -60.827625303

Reorder the terms:
50 + x = -60.827625303

Solving
50 + x = -60.827625303

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 = -60.827625303 + -50

Combine like terms: 50 + -50 = 0
0 + x = -60.827625303 + -50
x = -60.827625303 + -50

Combine like terms: -60.827625303 + -50 = -110.827625303
x = -110.827625303

Simplifying
x = -110.827625303


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.827625303, -110.827625303}
Solution
x = {10.827625303, -110.827625303}

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