x^2-14x-146=0

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Solution for x^2-14x-146=0 equation: 


Simplifying
x2 + -14x + -146 = 0

Reorder the terms:
-146 + -14x + x2 = 0

Solving
-146 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '146' to each side of the equation.
-146 + -14x + 146 + x2 = 0 + 146

Reorder the terms:
-146 + 146 + -14x + x2 = 0 + 146

Combine like terms: -146 + 146 = 0
0 + -14x + x2 = 0 + 146
-14x + x2 = 0 + 146

Combine like terms: 0 + 146 = 146
-14x + x2 = 146

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 = 146 + 49

Reorder the terms:
49 + -14x + x2 = 146 + 49

Combine like terms: 146 + 49 = 195
49 + -14x + x2 = 195

Factor a perfect square on the left side:
(x + -7)(x + -7) = 195

Calculate the square root of the right side: 13.964240044

Break this problem into two subproblems by setting 
(x + -7) equal to 13.964240044 and -13.964240044.


Subproblem 1
x + -7 = 13.964240044

Simplifying
x + -7 = 13.964240044

Reorder the terms:
-7 + x = 13.964240044

Solving
-7 + x = 13.964240044

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 = 13.964240044 + 7

Combine like terms: -7 + 7 = 0
0 + x = 13.964240044 + 7
x = 13.964240044 + 7

Combine like terms: 13.964240044 + 7 = 20.964240044
x = 20.964240044

Simplifying
x = 20.964240044


Subproblem 2
x + -7 = -13.964240044

Simplifying
x + -7 = -13.964240044

Reorder the terms:
-7 + x = -13.964240044

Solving
-7 + x = -13.964240044

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 = -13.964240044 + 7

Combine like terms: -7 + 7 = 0
0 + x = -13.964240044 + 7
x = -13.964240044 + 7

Combine like terms: -13.964240044 + 7 = -6.964240044
x = -6.964240044

Simplifying
x = -6.964240044


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.964240044, -6.964240044}

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