2x^2-40x-100=0

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Solution for 2x^2-40x-100=0 equation: 


Simplifying
2x2 + -40x + -100 = 0

Reorder the terms:
-100 + -40x + 2x2 = 0

Solving
-100 + -40x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + -20x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + -20x + x2)' equal to zero and attempt to solve:

Simplifying
-50 + -20x + x2 = 0

Solving
-50 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -20x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -20x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -20x + x2 = 0 + 50
-20x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-20x + x2 = 50

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 = 50 + 100

Reorder the terms:
100 + -20x + x2 = 50 + 100

Combine like terms: 50 + 100 = 150
100 + -20x + x2 = 150

Factor a perfect square on the left side:
(x + -10)(x + -10) = 150

Calculate the square root of the right side: 12.247448714

Break this problem into two subproblems by setting 
(x + -10) equal to 12.247448714 and -12.247448714.


Subproblem 1
x + -10 = 12.247448714

Simplifying
x + -10 = 12.247448714

Reorder the terms:
-10 + x = 12.247448714

Solving
-10 + x = 12.247448714

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 = 12.247448714 + 10

Combine like terms: -10 + 10 = 0
0 + x = 12.247448714 + 10
x = 12.247448714 + 10

Combine like terms: 12.247448714 + 10 = 22.247448714
x = 22.247448714

Simplifying
x = 22.247448714


Subproblem 2
x + -10 = -12.247448714

Simplifying
x + -10 = -12.247448714

Reorder the terms:
-10 + x = -12.247448714

Solving
-10 + x = -12.247448714

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 = -12.247448714 + 10

Combine like terms: -10 + 10 = 0
0 + x = -12.247448714 + 10
x = -12.247448714 + 10

Combine like terms: -12.247448714 + 10 = -2.247448714
x = -2.247448714

Simplifying
x = -2.247448714


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.247448714, -2.247448714}
Solution
x = {22.247448714, -2.247448714}

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