x^2+676x-11840=0

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Solution for x^2+676x-11840=0 equation: 


Simplifying
x2 + 676x + -11840 = 0

Reorder the terms:
-11840 + 676x + x2 = 0

Solving
-11840 + 676x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '11840' to each side of the equation.
-11840 + 676x + 11840 + x2 = 0 + 11840

Reorder the terms:
-11840 + 11840 + 676x + x2 = 0 + 11840

Combine like terms: -11840 + 11840 = 0
0 + 676x + x2 = 0 + 11840
676x + x2 = 0 + 11840

Combine like terms: 0 + 11840 = 11840
676x + x2 = 11840

The x term is 676x.  Take half its coefficient (338).
Square it (114244) and add it to both sides.

Add '114244' to each side of the equation.
676x + 114244 + x2 = 11840 + 114244

Reorder the terms:
114244 + 676x + x2 = 11840 + 114244

Combine like terms: 11840 + 114244 = 126084
114244 + 676x + x2 = 126084

Factor a perfect square on the left side:
(x + 338)(x + 338) = 126084

Calculate the square root of the right side: 355.083088868

Break this problem into two subproblems by setting 
(x + 338) equal to 355.083088868 and -355.083088868.


Subproblem 1
x + 338 = 355.083088868

Simplifying
x + 338 = 355.083088868

Reorder the terms:
338 + x = 355.083088868

Solving
338 + x = 355.083088868

Solving for variable 'x'.

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

Add '-338' to each side of the equation.
338 + -338 + x = 355.083088868 + -338

Combine like terms: 338 + -338 = 0
0 + x = 355.083088868 + -338
x = 355.083088868 + -338

Combine like terms: 355.083088868 + -338 = 17.083088868
x = 17.083088868

Simplifying
x = 17.083088868


Subproblem 2
x + 338 = -355.083088868

Simplifying
x + 338 = -355.083088868

Reorder the terms:
338 + x = -355.083088868

Solving
338 + x = -355.083088868

Solving for variable 'x'.

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

Add '-338' to each side of the equation.
338 + -338 + x = -355.083088868 + -338

Combine like terms: 338 + -338 = 0
0 + x = -355.083088868 + -338
x = -355.083088868 + -338

Combine like terms: -355.083088868 + -338 = -693.083088868
x = -693.083088868

Simplifying
x = -693.083088868


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.083088868, -693.083088868}

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