2x^2-4x-78=0

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Solution for 2x^2-4x-78=0 equation: 


Simplifying
2x2 + -4x + -78 = 0

Reorder the terms:
-78 + -4x + 2x2 = 0

Solving
-78 + -4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-39 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-39 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-39 + -2x + x2 = 0

Solving
-39 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + -2x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + -2x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -2x + x2 = 0 + 39
-2x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
-2x + x2 = 39

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 39 + 1

Reorder the terms:
1 + -2x + x2 = 39 + 1

Combine like terms: 39 + 1 = 40
1 + -2x + x2 = 40

Factor a perfect square on the left side:
(x + -1)(x + -1) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -1) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + -1 = 6.32455532

Simplifying
x + -1 = 6.32455532

Reorder the terms:
-1 + x = 6.32455532

Solving
-1 + x = 6.32455532

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 6.32455532 + 1

Combine like terms: -1 + 1 = 0
0 + x = 6.32455532 + 1
x = 6.32455532 + 1

Combine like terms: 6.32455532 + 1 = 7.32455532
x = 7.32455532

Simplifying
x = 7.32455532


Subproblem 2
x + -1 = -6.32455532

Simplifying
x + -1 = -6.32455532

Reorder the terms:
-1 + x = -6.32455532

Solving
-1 + x = -6.32455532

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -6.32455532 + 1

Combine like terms: -1 + 1 = 0
0 + x = -6.32455532 + 1
x = -6.32455532 + 1

Combine like terms: -6.32455532 + 1 = -5.32455532
x = -5.32455532

Simplifying
x = -5.32455532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.32455532, -5.32455532}
Solution
x = {7.32455532, -5.32455532}

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