8x^2-38x+10=0

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Solution for 8x^2-38x+10=0 equation: 


Simplifying
8x2 + -38x + 10 = 0

Reorder the terms:
10 + -38x + 8x2 = 0

Solving
10 + -38x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -19x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -19x + 4x2)' equal to zero and attempt to solve:

Simplifying
5 + -19x + 4x2 = 0

Solving
5 + -19x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
1.25 + -4.75x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -4.75x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -4.75x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -4.75x + x2 = 0 + -1.25
-4.75x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-4.75x + x2 = -1.25

The x term is -4.75x.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75x + 5.640625 + x2 = -1.25 + 5.640625

Reorder the terms:
5.640625 + -4.75x + x2 = -1.25 + 5.640625

Combine like terms: -1.25 + 5.640625 = 4.390625
5.640625 + -4.75x + x2 = 4.390625

Factor a perfect square on the left side:
(x + -2.375)(x + -2.375) = 4.390625

Calculate the square root of the right side: 2.095381827

Break this problem into two subproblems by setting 
(x + -2.375) equal to 2.095381827 and -2.095381827.


Subproblem 1
x + -2.375 = 2.095381827

Simplifying
x + -2.375 = 2.095381827

Reorder the terms:
-2.375 + x = 2.095381827

Solving
-2.375 + x = 2.095381827

Solving for variable 'x'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + x = 2.095381827 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + x = 2.095381827 + 2.375
x = 2.095381827 + 2.375

Combine like terms: 2.095381827 + 2.375 = 4.470381827
x = 4.470381827

Simplifying
x = 4.470381827


Subproblem 2
x + -2.375 = -2.095381827

Simplifying
x + -2.375 = -2.095381827

Reorder the terms:
-2.375 + x = -2.095381827

Solving
-2.375 + x = -2.095381827

Solving for variable 'x'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + x = -2.095381827 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + x = -2.095381827 + 2.375
x = -2.095381827 + 2.375

Combine like terms: -2.095381827 + 2.375 = 0.279618173
x = 0.279618173

Simplifying
x = 0.279618173


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.470381827, 0.279618173}
Solution
x = {4.470381827, 0.279618173}

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