2x^2-12x-52=0

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Solution for 2x^2-12x-52=0 equation: 


Simplifying
2x2 + -12x + -52 = 0

Reorder the terms:
-52 + -12x + 2x2 = 0

Solving
-52 + -12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-26 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-26 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-26 + -6x + x2 = 0

Solving
-26 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + -6x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + -6x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -6x + x2 = 0 + 26
-6x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
-6x + x2 = 26

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 26 + 9

Reorder the terms:
9 + -6x + x2 = 26 + 9

Combine like terms: 26 + 9 = 35
9 + -6x + x2 = 35

Factor a perfect square on the left side:
(x + -3)(x + -3) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(x + -3) equal to 5.916079783 and -5.916079783.


Subproblem 1
x + -3 = 5.916079783

Simplifying
x + -3 = 5.916079783

Reorder the terms:
-3 + x = 5.916079783

Solving
-3 + x = 5.916079783

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 5.916079783 + 3

Combine like terms: -3 + 3 = 0
0 + x = 5.916079783 + 3
x = 5.916079783 + 3

Combine like terms: 5.916079783 + 3 = 8.916079783
x = 8.916079783

Simplifying
x = 8.916079783


Subproblem 2
x + -3 = -5.916079783

Simplifying
x + -3 = -5.916079783

Reorder the terms:
-3 + x = -5.916079783

Solving
-3 + x = -5.916079783

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -5.916079783 + 3

Combine like terms: -3 + 3 = 0
0 + x = -5.916079783 + 3
x = -5.916079783 + 3

Combine like terms: -5.916079783 + 3 = -2.916079783
x = -2.916079783

Simplifying
x = -2.916079783


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.916079783, -2.916079783}
Solution
x = {8.916079783, -2.916079783}

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