x^2+163x-6552=0

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Solution for x^2+163x-6552=0 equation: 


Simplifying
x2 + 163x + -6552 = 0

Reorder the terms:
-6552 + 163x + x2 = 0

Solving
-6552 + 163x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '6552' to each side of the equation.
-6552 + 163x + 6552 + x2 = 0 + 6552

Reorder the terms:
-6552 + 6552 + 163x + x2 = 0 + 6552

Combine like terms: -6552 + 6552 = 0
0 + 163x + x2 = 0 + 6552
163x + x2 = 0 + 6552

Combine like terms: 0 + 6552 = 6552
163x + x2 = 6552

The x term is 163x.  Take half its coefficient (81.5).
Square it (6642.25) and add it to both sides.

Add '6642.25' to each side of the equation.
163x + 6642.25 + x2 = 6552 + 6642.25

Reorder the terms:
6642.25 + 163x + x2 = 6552 + 6642.25

Combine like terms: 6552 + 6642.25 = 13194.25
6642.25 + 163x + x2 = 13194.25

Factor a perfect square on the left side:
(x + 81.5)(x + 81.5) = 13194.25

Calculate the square root of the right side: 114.866226542

Break this problem into two subproblems by setting 
(x + 81.5) equal to 114.866226542 and -114.866226542.


Subproblem 1
x + 81.5 = 114.866226542

Simplifying
x + 81.5 = 114.866226542

Reorder the terms:
81.5 + x = 114.866226542

Solving
81.5 + x = 114.866226542

Solving for variable 'x'.

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

Add '-81.5' to each side of the equation.
81.5 + -81.5 + x = 114.866226542 + -81.5

Combine like terms: 81.5 + -81.5 = 0.0
0.0 + x = 114.866226542 + -81.5
x = 114.866226542 + -81.5

Combine like terms: 114.866226542 + -81.5 = 33.366226542
x = 33.366226542

Simplifying
x = 33.366226542


Subproblem 2
x + 81.5 = -114.866226542

Simplifying
x + 81.5 = -114.866226542

Reorder the terms:
81.5 + x = -114.866226542

Solving
81.5 + x = -114.866226542

Solving for variable 'x'.

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

Add '-81.5' to each side of the equation.
81.5 + -81.5 + x = -114.866226542 + -81.5

Combine like terms: 81.5 + -81.5 = 0.0
0.0 + x = -114.866226542 + -81.5
x = -114.866226542 + -81.5

Combine like terms: -114.866226542 + -81.5 = -196.366226542
x = -196.366226542

Simplifying
x = -196.366226542


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {33.366226542, -196.366226542}

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