2x^2+4x-1008=0

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Solution for 2x^2+4x-1008=0 equation:


Simplifying
2x2 + 4x + -1008 = 0

Reorder the terms:
-1008 + 4x + 2x2 = 0

Solving
-1008 + 4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-504 + 2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-504 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-504 + 2x + x2 = 0

Solving
-504 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '504' to each side of the equation.
-504 + 2x + 504 + x2 = 0 + 504

Reorder the terms:
-504 + 504 + 2x + x2 = 0 + 504

Combine like terms: -504 + 504 = 0
0 + 2x + x2 = 0 + 504
2x + x2 = 0 + 504

Combine like terms: 0 + 504 = 504
2x + x2 = 504

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 504 + 1

Reorder the terms:
1 + 2x + x2 = 504 + 1

Combine like terms: 504 + 1 = 505
1 + 2x + x2 = 505

Factor a perfect square on the left side:
(x + 1)(x + 1) = 505

Calculate the square root of the right side: 22.472205054

Break this problem into two subproblems by setting 
(x + 1) equal to 22.472205054 and -22.472205054.


Subproblem 1
x + 1 = 22.472205054

Simplifying
x + 1 = 22.472205054

Reorder the terms:
1 + x = 22.472205054

Solving
1 + x = 22.472205054

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 22.472205054 + -1

Combine like terms: 1 + -1 = 0
0 + x = 22.472205054 + -1
x = 22.472205054 + -1

Combine like terms: 22.472205054 + -1 = 21.472205054
x = 21.472205054

Simplifying
x = 21.472205054


Subproblem 2
x + 1 = -22.472205054

Simplifying
x + 1 = -22.472205054

Reorder the terms:
1 + x = -22.472205054

Solving
1 + x = -22.472205054

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -22.472205054 + -1

Combine like terms: 1 + -1 = 0
0 + x = -22.472205054 + -1
x = -22.472205054 + -1

Combine like terms: -22.472205054 + -1 = -23.472205054
x = -23.472205054

Simplifying
x = -23.472205054


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.472205054, -23.472205054}
Solution
x = {21.472205054, -23.472205054}

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