2x^2-40x-284=0

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Solution for 2x^2-40x-284=0 equation: 


Simplifying
2x2 + -40x + -284 = 0

Reorder the terms:
-284 + -40x + 2x2 = 0

Solving
-284 + -40x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-142 + -20x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-142 + -20x + x2)' equal to zero and attempt to solve:

Simplifying
-142 + -20x + x2 = 0

Solving
-142 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '142' to each side of the equation.
-142 + -20x + 142 + x2 = 0 + 142

Reorder the terms:
-142 + 142 + -20x + x2 = 0 + 142

Combine like terms: -142 + 142 = 0
0 + -20x + x2 = 0 + 142
-20x + x2 = 0 + 142

Combine like terms: 0 + 142 = 142
-20x + x2 = 142

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 142 + 100

Reorder the terms:
100 + -20x + x2 = 142 + 100

Combine like terms: 142 + 100 = 242
100 + -20x + x2 = 242

Factor a perfect square on the left side:
(x + -10)(x + -10) = 242

Calculate the square root of the right side: 15.556349186

Break this problem into two subproblems by setting 
(x + -10) equal to 15.556349186 and -15.556349186.


Subproblem 1
x + -10 = 15.556349186

Simplifying
x + -10 = 15.556349186

Reorder the terms:
-10 + x = 15.556349186

Solving
-10 + x = 15.556349186

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 15.556349186 + 10

Combine like terms: -10 + 10 = 0
0 + x = 15.556349186 + 10
x = 15.556349186 + 10

Combine like terms: 15.556349186 + 10 = 25.556349186
x = 25.556349186

Simplifying
x = 25.556349186


Subproblem 2
x + -10 = -15.556349186

Simplifying
x + -10 = -15.556349186

Reorder the terms:
-10 + x = -15.556349186

Solving
-10 + x = -15.556349186

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -15.556349186 + 10

Combine like terms: -10 + 10 = 0
0 + x = -15.556349186 + 10
x = -15.556349186 + 10

Combine like terms: -15.556349186 + 10 = -5.556349186
x = -5.556349186

Simplifying
x = -5.556349186


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.556349186, -5.556349186}
Solution
x = {25.556349186, -5.556349186}

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