x^2-4x-104=0

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Solution for x^2-4x-104=0 equation:


Simplifying
x2 + -4x + -104 = 0

Reorder the terms:
-104 + -4x + x2 = 0

Solving
-104 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '104' to each side of the equation.
-104 + -4x + 104 + x2 = 0 + 104

Reorder the terms:
-104 + 104 + -4x + x2 = 0 + 104

Combine like terms: -104 + 104 = 0
0 + -4x + x2 = 0 + 104
-4x + x2 = 0 + 104

Combine like terms: 0 + 104 = 104
-4x + x2 = 104

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 104 + 4

Reorder the terms:
4 + -4x + x2 = 104 + 4

Combine like terms: 104 + 4 = 108
4 + -4x + x2 = 108

Factor a perfect square on the left side:
(x + -2)(x + -2) = 108

Calculate the square root of the right side: 10.392304845

Break this problem into two subproblems by setting 
(x + -2) equal to 10.392304845 and -10.392304845.

Subproblem 1

x + -2 = 10.392304845 Simplifying x + -2 = 10.392304845 Reorder the terms: -2 + x = 10.392304845 Solving -2 + x = 10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 10.392304845 + 2 Combine like terms: -2 + 2 = 0 0 + x = 10.392304845 + 2 x = 10.392304845 + 2 Combine like terms: 10.392304845 + 2 = 12.392304845 x = 12.392304845 Simplifying x = 12.392304845

Subproblem 2

x + -2 = -10.392304845 Simplifying x + -2 = -10.392304845 Reorder the terms: -2 + x = -10.392304845 Solving -2 + x = -10.392304845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -10.392304845 + 2 Combine like terms: -2 + 2 = 0 0 + x = -10.392304845 + 2 x = -10.392304845 + 2 Combine like terms: -10.392304845 + 2 = -8.392304845 x = -8.392304845 Simplifying x = -8.392304845

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.392304845, -8.392304845}

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