4x^2-220x+180=0

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Solution for 4x^2-220x+180=0 equation: 


Simplifying
4x2 + -220x + 180 = 0

Reorder the terms:
180 + -220x + 4x2 = 0

Solving
180 + -220x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(45 + -55x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(45 + -55x + x2)' equal to zero and attempt to solve:

Simplifying
45 + -55x + x2 = 0

Solving
45 + -55x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -55x + -45 + x2 = 0 + -45

Reorder the terms:
45 + -45 + -55x + x2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -55x + x2 = 0 + -45
-55x + x2 = 0 + -45

Combine like terms: 0 + -45 = -45
-55x + x2 = -45

The x term is -55x.  Take half its coefficient (-27.5).
Square it (756.25) and add it to both sides.

Add '756.25' to each side of the equation.
-55x + 756.25 + x2 = -45 + 756.25

Reorder the terms:
756.25 + -55x + x2 = -45 + 756.25

Combine like terms: -45 + 756.25 = 711.25
756.25 + -55x + x2 = 711.25

Factor a perfect square on the left side:
(x + -27.5)(x + -27.5) = 711.25

Calculate the square root of the right side: 26.669270706

Break this problem into two subproblems by setting 
(x + -27.5) equal to 26.669270706 and -26.669270706.


Subproblem 1
x + -27.5 = 26.669270706

Simplifying
x + -27.5 = 26.669270706

Reorder the terms:
-27.5 + x = 26.669270706

Solving
-27.5 + x = 26.669270706

Solving for variable 'x'.

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

Add '27.5' to each side of the equation.
-27.5 + 27.5 + x = 26.669270706 + 27.5

Combine like terms: -27.5 + 27.5 = 0.0
0.0 + x = 26.669270706 + 27.5
x = 26.669270706 + 27.5

Combine like terms: 26.669270706 + 27.5 = 54.169270706
x = 54.169270706

Simplifying
x = 54.169270706


Subproblem 2
x + -27.5 = -26.669270706

Simplifying
x + -27.5 = -26.669270706

Reorder the terms:
-27.5 + x = -26.669270706

Solving
-27.5 + x = -26.669270706

Solving for variable 'x'.

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

Add '27.5' to each side of the equation.
-27.5 + 27.5 + x = -26.669270706 + 27.5

Combine like terms: -27.5 + 27.5 = 0.0
0.0 + x = -26.669270706 + 27.5
x = -26.669270706 + 27.5

Combine like terms: -26.669270706 + 27.5 = 0.830729294
x = 0.830729294

Simplifying
x = 0.830729294


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {54.169270706, 0.830729294}
Solution
x = {54.169270706, 0.830729294}

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