x^2-14x-3430=0

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Solution for x^2-14x-3430=0 equation: 


Simplifying
x2 + -14x + -3430 = 0

Reorder the terms:
-3430 + -14x + x2 = 0

Solving
-3430 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3430' to each side of the equation.
-3430 + -14x + 3430 + x2 = 0 + 3430

Reorder the terms:
-3430 + 3430 + -14x + x2 = 0 + 3430

Combine like terms: -3430 + 3430 = 0
0 + -14x + x2 = 0 + 3430
-14x + x2 = 0 + 3430

Combine like terms: 0 + 3430 = 3430
-14x + x2 = 3430

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 = 3430 + 49

Reorder the terms:
49 + -14x + x2 = 3430 + 49

Combine like terms: 3430 + 49 = 3479
49 + -14x + x2 = 3479

Factor a perfect square on the left side:
(x + -7)(x + -7) = 3479

Calculate the square root of the right side: 58.983048412

Break this problem into two subproblems by setting 
(x + -7) equal to 58.983048412 and -58.983048412.


Subproblem 1
x + -7 = 58.983048412

Simplifying
x + -7 = 58.983048412

Reorder the terms:
-7 + x = 58.983048412

Solving
-7 + x = 58.983048412

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 = 58.983048412 + 7

Combine like terms: -7 + 7 = 0
0 + x = 58.983048412 + 7
x = 58.983048412 + 7

Combine like terms: 58.983048412 + 7 = 65.983048412
x = 65.983048412

Simplifying
x = 65.983048412


Subproblem 2
x + -7 = -58.983048412

Simplifying
x + -7 = -58.983048412

Reorder the terms:
-7 + x = -58.983048412

Solving
-7 + x = -58.983048412

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 = -58.983048412 + 7

Combine like terms: -7 + 7 = 0
0 + x = -58.983048412 + 7
x = -58.983048412 + 7

Combine like terms: -58.983048412 + 7 = -51.983048412
x = -51.983048412

Simplifying
x = -51.983048412


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {65.983048412, -51.983048412}

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