-2x^2+10x-1=0

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Solution for -2x^2+10x-1=0 equation: 


Simplifying
-2x2 + 10x + -1 = 0

Reorder the terms:
-1 + 10x + -2x2 = 0

Solving
-1 + 10x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
0.5 + -5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -5x + x2 = 0 + -0.5
-5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-5x + x2 = -0.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -0.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -0.5 + 6.25

Combine like terms: -0.5 + 6.25 = 5.75
6.25 + -5x + x2 = 5.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.397915762 and -2.397915762.


Subproblem 1
x + -2.5 = 2.397915762

Simplifying
x + -2.5 = 2.397915762

Reorder the terms:
-2.5 + x = 2.397915762

Solving
-2.5 + x = 2.397915762

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 2.397915762 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.397915762 + 2.5
x = 2.397915762 + 2.5

Combine like terms: 2.397915762 + 2.5 = 4.897915762
x = 4.897915762

Simplifying
x = 4.897915762


Subproblem 2
x + -2.5 = -2.397915762

Simplifying
x + -2.5 = -2.397915762

Reorder the terms:
-2.5 + x = -2.397915762

Solving
-2.5 + x = -2.397915762

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -2.397915762 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.397915762 + 2.5
x = -2.397915762 + 2.5

Combine like terms: -2.397915762 + 2.5 = 0.102084238
x = 0.102084238

Simplifying
x = 0.102084238


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.897915762, 0.102084238}

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