5x(x-4)=80

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Solution for 5x(x-4)=80 equation: 


Simplifying
5x(x + -4) = 80

Reorder the terms:
5x(-4 + x) = 80
(-4 * 5x + x * 5x) = 80
(-20x + 5x2) = 80

Solving
-20x + 5x2 = 80

Solving for variable 'x'.

Reorder the terms:
-80 + -20x + 5x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + -20x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-16 + -4x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-16 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + -4x + x2 = 0

Solving
-16 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -4x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -4x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -4x + x2 = 0 + 16
-4x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-4x + x2 = 16

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 = 16 + 4

Reorder the terms:
4 + -4x + x2 = 16 + 4

Combine like terms: 16 + 4 = 20
4 + -4x + x2 = 20

Factor a perfect square on the left side:
(x + -2)(x + -2) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + -2) equal to 4.472135955 and -4.472135955.


Subproblem 1
x + -2 = 4.472135955

Simplifying
x + -2 = 4.472135955

Reorder the terms:
-2 + x = 4.472135955

Solving
-2 + x = 4.472135955

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 = 4.472135955 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.472135955 + 2
x = 4.472135955 + 2

Combine like terms: 4.472135955 + 2 = 6.472135955
x = 6.472135955

Simplifying
x = 6.472135955


Subproblem 2
x + -2 = -4.472135955

Simplifying
x + -2 = -4.472135955

Reorder the terms:
-2 + x = -4.472135955

Solving
-2 + x = -4.472135955

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 = -4.472135955 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.472135955 + 2
x = -4.472135955 + 2

Combine like terms: -4.472135955 + 2 = -2.472135955
x = -2.472135955

Simplifying
x = -2.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.472135955, -2.472135955}
Solution
x = {6.472135955, -2.472135955}

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