2x^2-20x+28=0

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Solution for 2x^2-20x+28=0 equation: 


Simplifying
2x2 + -20x + 28 = 0

Reorder the terms:
28 + -20x + 2x2 = 0

Solving
28 + -20x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -10x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(14 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
14 + -10x + x2 = 0

Solving
14 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -10x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + -10x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -10x + x2 = 0 + -14
-10x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
-10x + x2 = -14

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -14 + 25

Reorder the terms:
25 + -10x + x2 = -14 + 25

Combine like terms: -14 + 25 = 11
25 + -10x + x2 = 11

Factor a perfect square on the left side:
(x + -5)(x + -5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -5) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + -5 = 3.31662479

Simplifying
x + -5 = 3.31662479

Reorder the terms:
-5 + x = 3.31662479

Solving
-5 + x = 3.31662479

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 3.31662479 + 5

Combine like terms: -5 + 5 = 0
0 + x = 3.31662479 + 5
x = 3.31662479 + 5

Combine like terms: 3.31662479 + 5 = 8.31662479
x = 8.31662479

Simplifying
x = 8.31662479


Subproblem 2
x + -5 = -3.31662479

Simplifying
x + -5 = -3.31662479

Reorder the terms:
-5 + x = -3.31662479

Solving
-5 + x = -3.31662479

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -3.31662479 + 5

Combine like terms: -5 + 5 = 0
0 + x = -3.31662479 + 5
x = -3.31662479 + 5

Combine like terms: -3.31662479 + 5 = 1.68337521
x = 1.68337521

Simplifying
x = 1.68337521


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.31662479, 1.68337521}
Solution
x = {8.31662479, 1.68337521}

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