x^2-5x-4356=0

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Solution for x^2-5x-4356=0 equation:


Simplifying
x2 + -5x + -4356 = 0

Reorder the terms:
-4356 + -5x + x2 = 0

Solving
-4356 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4356' to each side of the equation.
-4356 + -5x + 4356 + x2 = 0 + 4356

Reorder the terms:
-4356 + 4356 + -5x + x2 = 0 + 4356

Combine like terms: -4356 + 4356 = 0
0 + -5x + x2 = 0 + 4356
-5x + x2 = 0 + 4356

Combine like terms: 0 + 4356 = 4356
-5x + x2 = 4356

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 4356 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 4356 + 6.25

Combine like terms: 4356 + 6.25 = 4362.25
6.25 + -5x + x2 = 4362.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 4362.25

Calculate the square root of the right side: 66.047331513

Break this problem into two subproblems by setting 
(x + -2.5) equal to 66.047331513 and -66.047331513.


Subproblem 1
x + -2.5 = 66.047331513

Simplifying
x + -2.5 = 66.047331513

Reorder the terms:
-2.5 + x = 66.047331513

Solving
-2.5 + x = 66.047331513

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 66.047331513 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 66.047331513 + 2.5
x = 66.047331513 + 2.5

Combine like terms: 66.047331513 + 2.5 = 68.547331513
x = 68.547331513

Simplifying
x = 68.547331513


Subproblem 2
x + -2.5 = -66.047331513

Simplifying
x + -2.5 = -66.047331513

Reorder the terms:
-2.5 + x = -66.047331513

Solving
-2.5 + x = -66.047331513

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -66.047331513 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -66.047331513 + 2.5
x = -66.047331513 + 2.5

Combine like terms: -66.047331513 + 2.5 = -63.547331513
x = -63.547331513

Simplifying
x = -63.547331513


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {68.547331513, -63.547331513}

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