1x(4x-20)=180

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Solution for 1x(4x-20)=180 equation: 


Simplifying
1x(4x + -20) = 180

Reorder the terms:
1x(-20 + 4x) = 180
(-20 * 1x + 4x * 1x) = 180
(-20x + 4x2) = 180

Solving
-20x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -20x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + -5x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + -5x + x2 = 0

Solving
-45 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -5x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + -5x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -5x + x2 = 0 + 45
-5x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
-5x + x2 = 45

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 45 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 45 + 6.25

Combine like terms: 45 + 6.25 = 51.25
6.25 + -5x + x2 = 51.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 51.25

Calculate the square root of the right side: 7.158910532

Break this problem into two subproblems by setting 
(x + -2.5) equal to 7.158910532 and -7.158910532.


Subproblem 1
x + -2.5 = 7.158910532

Simplifying
x + -2.5 = 7.158910532

Reorder the terms:
-2.5 + x = 7.158910532

Solving
-2.5 + x = 7.158910532

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 7.158910532 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 7.158910532 + 2.5
x = 7.158910532 + 2.5

Combine like terms: 7.158910532 + 2.5 = 9.658910532
x = 9.658910532

Simplifying
x = 9.658910532


Subproblem 2
x + -2.5 = -7.158910532

Simplifying
x + -2.5 = -7.158910532

Reorder the terms:
-2.5 + x = -7.158910532

Solving
-2.5 + x = -7.158910532

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -7.158910532 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -7.158910532 + 2.5
x = -7.158910532 + 2.5

Combine like terms: -7.158910532 + 2.5 = -4.658910532
x = -4.658910532

Simplifying
x = -4.658910532


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.658910532, -4.658910532}
Solution
x = {9.658910532, -4.658910532}

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