x^2+14x-1568=0

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Solution for x^2+14x-1568=0 equation: 


Simplifying
x2 + 14x + -1568 = 0

Reorder the terms:
-1568 + 14x + x2 = 0

Solving
-1568 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1568' to each side of the equation.
-1568 + 14x + 1568 + x2 = 0 + 1568

Reorder the terms:
-1568 + 1568 + 14x + x2 = 0 + 1568

Combine like terms: -1568 + 1568 = 0
0 + 14x + x2 = 0 + 1568
14x + x2 = 0 + 1568

Combine like terms: 0 + 1568 = 1568
14x + x2 = 1568

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 1568 + 49

Reorder the terms:
49 + 14x + x2 = 1568 + 49

Combine like terms: 1568 + 49 = 1617
49 + 14x + x2 = 1617

Factor a perfect square on the left side:
(x + 7)(x + 7) = 1617

Calculate the square root of the right side: 40.211938526

Break this problem into two subproblems by setting 
(x + 7) equal to 40.211938526 and -40.211938526.


Subproblem 1
x + 7 = 40.211938526

Simplifying
x + 7 = 40.211938526

Reorder the terms:
7 + x = 40.211938526

Solving
7 + x = 40.211938526

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 40.211938526 + -7

Combine like terms: 7 + -7 = 0
0 + x = 40.211938526 + -7
x = 40.211938526 + -7

Combine like terms: 40.211938526 + -7 = 33.211938526
x = 33.211938526

Simplifying
x = 33.211938526


Subproblem 2
x + 7 = -40.211938526

Simplifying
x + 7 = -40.211938526

Reorder the terms:
7 + x = -40.211938526

Solving
7 + x = -40.211938526

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -40.211938526 + -7

Combine like terms: 7 + -7 = 0
0 + x = -40.211938526 + -7
x = -40.211938526 + -7

Combine like terms: -40.211938526 + -7 = -47.211938526
x = -47.211938526

Simplifying
x = -47.211938526


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {33.211938526, -47.211938526}

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