x^2-14x-165.25=0

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Solution for x^2-14x-165.25=0 equation: 


Simplifying
x2 + -14x + -165.25 = 0

Reorder the terms:
-165.25 + -14x + x2 = 0

Solving
-165.25 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '165.25' to each side of the equation.
-165.25 + -14x + 165.25 + x2 = 0 + 165.25

Reorder the terms:
-165.25 + 165.25 + -14x + x2 = 0 + 165.25

Combine like terms: -165.25 + 165.25 = 0.00
0.00 + -14x + x2 = 0 + 165.25
-14x + x2 = 0 + 165.25

Combine like terms: 0 + 165.25 = 165.25
-14x + x2 = 165.25

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 = 165.25 + 49

Reorder the terms:
49 + -14x + x2 = 165.25 + 49

Combine like terms: 165.25 + 49 = 214.25
49 + -14x + x2 = 214.25

Factor a perfect square on the left side:
(x + -7)(x + -7) = 214.25

Calculate the square root of the right side: 14.637281168

Break this problem into two subproblems by setting 
(x + -7) equal to 14.637281168 and -14.637281168.


Subproblem 1
x + -7 = 14.637281168

Simplifying
x + -7 = 14.637281168

Reorder the terms:
-7 + x = 14.637281168

Solving
-7 + x = 14.637281168

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 = 14.637281168 + 7

Combine like terms: -7 + 7 = 0
0 + x = 14.637281168 + 7
x = 14.637281168 + 7

Combine like terms: 14.637281168 + 7 = 21.637281168
x = 21.637281168

Simplifying
x = 21.637281168


Subproblem 2
x + -7 = -14.637281168

Simplifying
x + -7 = -14.637281168

Reorder the terms:
-7 + x = -14.637281168

Solving
-7 + x = -14.637281168

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 = -14.637281168 + 7

Combine like terms: -7 + 7 = 0
0 + x = -14.637281168 + 7
x = -14.637281168 + 7

Combine like terms: -14.637281168 + 7 = -7.637281168
x = -7.637281168

Simplifying
x = -7.637281168


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.637281168, -7.637281168}

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