2x^2-102x+14=0

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Solution for 2x^2-102x+14=0 equation: 


Simplifying
2x2 + -102x + 14 = 0

Reorder the terms:
14 + -102x + 2x2 = 0

Solving
14 + -102x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -51x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -51x + x2)' equal to zero and attempt to solve:

Simplifying
7 + -51x + x2 = 0

Solving
7 + -51x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -51x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -51x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -51x + x2 = 0 + -7
-51x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-51x + x2 = -7

The x term is -51x.  Take half its coefficient (-25.5).
Square it (650.25) and add it to both sides.

Add '650.25' to each side of the equation.
-51x + 650.25 + x2 = -7 + 650.25

Reorder the terms:
650.25 + -51x + x2 = -7 + 650.25

Combine like terms: -7 + 650.25 = 643.25
650.25 + -51x + x2 = 643.25

Factor a perfect square on the left side:
(x + -25.5)(x + -25.5) = 643.25

Calculate the square root of the right side: 25.362373706

Break this problem into two subproblems by setting 
(x + -25.5) equal to 25.362373706 and -25.362373706.


Subproblem 1
x + -25.5 = 25.362373706

Simplifying
x + -25.5 = 25.362373706

Reorder the terms:
-25.5 + x = 25.362373706

Solving
-25.5 + x = 25.362373706

Solving for variable 'x'.

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

Add '25.5' to each side of the equation.
-25.5 + 25.5 + x = 25.362373706 + 25.5

Combine like terms: -25.5 + 25.5 = 0.0
0.0 + x = 25.362373706 + 25.5
x = 25.362373706 + 25.5

Combine like terms: 25.362373706 + 25.5 = 50.862373706
x = 50.862373706

Simplifying
x = 50.862373706


Subproblem 2
x + -25.5 = -25.362373706

Simplifying
x + -25.5 = -25.362373706

Reorder the terms:
-25.5 + x = -25.362373706

Solving
-25.5 + x = -25.362373706

Solving for variable 'x'.

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

Add '25.5' to each side of the equation.
-25.5 + 25.5 + x = -25.362373706 + 25.5

Combine like terms: -25.5 + 25.5 = 0.0
0.0 + x = -25.362373706 + 25.5
x = -25.362373706 + 25.5

Combine like terms: -25.362373706 + 25.5 = 0.137626294
x = 0.137626294

Simplifying
x = 0.137626294


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {50.862373706, 0.137626294}
Solution
x = {50.862373706, 0.137626294}

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