5x^2-20x-100=0

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Solution for 5x^2-20x-100=0 equation: 


Simplifying
5x2 + -20x + -100 = 0

Reorder the terms:
-100 + -20x + 5x2 = 0

Solving
-100 + -20x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + -4x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-20 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + -4x + x2 = 0

Solving
-20 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -4x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -4x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -4x + x2 = 0 + 20
-4x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-4x + x2 = 20

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 20 + 4

Reorder the terms:
4 + -4x + x2 = 20 + 4

Combine like terms: 20 + 4 = 24
4 + -4x + x2 = 24

Factor a perfect square on the left side:
(x + -2)(x + -2) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + -2) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + -2 = 4.898979486

Simplifying
x + -2 = 4.898979486

Reorder the terms:
-2 + x = 4.898979486

Solving
-2 + x = 4.898979486

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 4.898979486 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.898979486 + 2
x = 4.898979486 + 2

Combine like terms: 4.898979486 + 2 = 6.898979486
x = 6.898979486

Simplifying
x = 6.898979486


Subproblem 2
x + -2 = -4.898979486

Simplifying
x + -2 = -4.898979486

Reorder the terms:
-2 + x = -4.898979486

Solving
-2 + x = -4.898979486

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -4.898979486 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.898979486 + 2
x = -4.898979486 + 2

Combine like terms: -4.898979486 + 2 = -2.898979486
x = -2.898979486

Simplifying
x = -2.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.898979486, -2.898979486}
Solution
x = {6.898979486, -2.898979486}

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