10x^2-20x-400=0

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Solution for 10x^2-20x-400=0 equation: 


Simplifying
10x2 + -20x + -400 = 0

Reorder the terms:
-400 + -20x + 10x2 = 0

Solving
-400 + -20x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-40 + -2x + x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-40 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-40 + -2x + x2 = 0

Solving
-40 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -2x + 40 + x2 = 0 + 40

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

Combine like terms: -40 + 40 = 0
0 + -2x + x2 = 0 + 40
-2x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-2x + x2 = 40

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 = 40 + 1

Reorder the terms:
1 + -2x + x2 = 40 + 1

Combine like terms: 40 + 1 = 41
1 + -2x + x2 = 41

Factor a perfect square on the left side:
(x + -1)(x + -1) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + -1) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + -1 = 6.403124237

Simplifying
x + -1 = 6.403124237

Reorder the terms:
-1 + x = 6.403124237

Solving
-1 + x = 6.403124237

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 = 6.403124237 + 1

Combine like terms: -1 + 1 = 0
0 + x = 6.403124237 + 1
x = 6.403124237 + 1

Combine like terms: 6.403124237 + 1 = 7.403124237
x = 7.403124237

Simplifying
x = 7.403124237


Subproblem 2
x + -1 = -6.403124237

Simplifying
x + -1 = -6.403124237

Reorder the terms:
-1 + x = -6.403124237

Solving
-1 + x = -6.403124237

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 = -6.403124237 + 1

Combine like terms: -1 + 1 = 0
0 + x = -6.403124237 + 1
x = -6.403124237 + 1

Combine like terms: -6.403124237 + 1 = -5.403124237
x = -5.403124237

Simplifying
x = -5.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.403124237, -5.403124237}
Solution
x = {7.403124237, -5.403124237}

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