2x^2-28x+10=0

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Solution for 2x^2-28x+10=0 equation: 


Simplifying
2x2 + -28x + 10 = 0

Reorder the terms:
10 + -28x + 2x2 = 0

Solving
10 + -28x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
5 + -14x + x2 = 0

Solving
5 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -14x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -14x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -14x + x2 = 0 + -5
-14x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-14x + x2 = -5

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -5 + 49

Reorder the terms:
49 + -14x + x2 = -5 + 49

Combine like terms: -5 + 49 = 44
49 + -14x + x2 = 44

Factor a perfect square on the left side:
(x + -7)(x + -7) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(x + -7) equal to 6.633249581 and -6.633249581.


Subproblem 1
x + -7 = 6.633249581

Simplifying
x + -7 = 6.633249581

Reorder the terms:
-7 + x = 6.633249581

Solving
-7 + x = 6.633249581

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 6.633249581 + 7

Combine like terms: -7 + 7 = 0
0 + x = 6.633249581 + 7
x = 6.633249581 + 7

Combine like terms: 6.633249581 + 7 = 13.633249581
x = 13.633249581

Simplifying
x = 13.633249581


Subproblem 2
x + -7 = -6.633249581

Simplifying
x + -7 = -6.633249581

Reorder the terms:
-7 + x = -6.633249581

Solving
-7 + x = -6.633249581

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -6.633249581 + 7

Combine like terms: -7 + 7 = 0
0 + x = -6.633249581 + 7
x = -6.633249581 + 7

Combine like terms: -6.633249581 + 7 = 0.366750419
x = 0.366750419

Simplifying
x = 0.366750419


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.633249581, 0.366750419}
Solution
x = {13.633249581, 0.366750419}

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