x^2-235x-548=0

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Solution for x^2-235x-548=0 equation: 


Simplifying
x2 + -235x + -548 = 0

Reorder the terms:
-548 + -235x + x2 = 0

Solving
-548 + -235x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '548' to each side of the equation.
-548 + -235x + 548 + x2 = 0 + 548

Reorder the terms:
-548 + 548 + -235x + x2 = 0 + 548

Combine like terms: -548 + 548 = 0
0 + -235x + x2 = 0 + 548
-235x + x2 = 0 + 548

Combine like terms: 0 + 548 = 548
-235x + x2 = 548

The x term is -235x.  Take half its coefficient (-117.5).
Square it (13806.25) and add it to both sides.

Add '13806.25' to each side of the equation.
-235x + 13806.25 + x2 = 548 + 13806.25

Reorder the terms:
13806.25 + -235x + x2 = 548 + 13806.25

Combine like terms: 548 + 13806.25 = 14354.25
13806.25 + -235x + x2 = 14354.25

Factor a perfect square on the left side:
(x + -117.5)(x + -117.5) = 14354.25

Calculate the square root of the right side: 119.809223351

Break this problem into two subproblems by setting 
(x + -117.5) equal to 119.809223351 and -119.809223351.


Subproblem 1
x + -117.5 = 119.809223351

Simplifying
x + -117.5 = 119.809223351

Reorder the terms:
-117.5 + x = 119.809223351

Solving
-117.5 + x = 119.809223351

Solving for variable 'x'.

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

Add '117.5' to each side of the equation.
-117.5 + 117.5 + x = 119.809223351 + 117.5

Combine like terms: -117.5 + 117.5 = 0.0
0.0 + x = 119.809223351 + 117.5
x = 119.809223351 + 117.5

Combine like terms: 119.809223351 + 117.5 = 237.309223351
x = 237.309223351

Simplifying
x = 237.309223351


Subproblem 2
x + -117.5 = -119.809223351

Simplifying
x + -117.5 = -119.809223351

Reorder the terms:
-117.5 + x = -119.809223351

Solving
-117.5 + x = -119.809223351

Solving for variable 'x'.

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

Add '117.5' to each side of the equation.
-117.5 + 117.5 + x = -119.809223351 + 117.5

Combine like terms: -117.5 + 117.5 = 0.0
0.0 + x = -119.809223351 + 117.5
x = -119.809223351 + 117.5

Combine like terms: -119.809223351 + 117.5 = -2.309223351
x = -2.309223351

Simplifying
x = -2.309223351


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {237.309223351, -2.309223351}

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