2x^2-20x-76=0

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Solution for 2x^2-20x-76=0 equation: 


Simplifying
2x2 + -20x + -76 = 0

Reorder the terms:
-76 + -20x + 2x2 = 0

Solving
-76 + -20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-38 + -10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-38 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-38 + -10x + x2 = 0

Solving
-38 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + -10x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + -10x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + -10x + x2 = 0 + 38
-10x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
-10x + x2 = 38

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 38 + 25

Reorder the terms:
25 + -10x + x2 = 38 + 25

Combine like terms: 38 + 25 = 63
25 + -10x + x2 = 63

Factor a perfect square on the left side:
(x + -5)(x + -5) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + -5) equal to 7.937253933 and -7.937253933.


Subproblem 1
x + -5 = 7.937253933

Simplifying
x + -5 = 7.937253933

Reorder the terms:
-5 + x = 7.937253933

Solving
-5 + x = 7.937253933

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 7.937253933 + 5

Combine like terms: -5 + 5 = 0
0 + x = 7.937253933 + 5
x = 7.937253933 + 5

Combine like terms: 7.937253933 + 5 = 12.937253933
x = 12.937253933

Simplifying
x = 12.937253933


Subproblem 2
x + -5 = -7.937253933

Simplifying
x + -5 = -7.937253933

Reorder the terms:
-5 + x = -7.937253933

Solving
-5 + x = -7.937253933

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -7.937253933 + 5

Combine like terms: -5 + 5 = 0
0 + x = -7.937253933 + 5
x = -7.937253933 + 5

Combine like terms: -7.937253933 + 5 = -2.937253933
x = -2.937253933

Simplifying
x = -2.937253933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.937253933, -2.937253933}
Solution
x = {12.937253933, -2.937253933}

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