x^2-4.25x+2=0

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Solution for x^2-4.25x+2=0 equation: 


Simplifying
x2 + -4.25x + 2 = 0

Reorder the terms:
2 + -4.25x + x2 = 0

Solving
2 + -4.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4.25x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -4.25x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4.25x + x2 = 0 + -2
-4.25x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4.25x + x2 = -2

The x term is -4.25x.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25x + 4.515625 + x2 = -2 + 4.515625

Reorder the terms:
4.515625 + -4.25x + x2 = -2 + 4.515625

Combine like terms: -2 + 4.515625 = 2.515625
4.515625 + -4.25x + x2 = 2.515625

Factor a perfect square on the left side:
(x + -2.125)(x + -2.125) = 2.515625

Calculate the square root of the right side: 1.586072193

Break this problem into two subproblems by setting 
(x + -2.125) equal to 1.586072193 and -1.586072193.


Subproblem 1
x + -2.125 = 1.586072193

Simplifying
x + -2.125 = 1.586072193

Reorder the terms:
-2.125 + x = 1.586072193

Solving
-2.125 + x = 1.586072193

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x = 1.586072193 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = 1.586072193 + 2.125
x = 1.586072193 + 2.125

Combine like terms: 1.586072193 + 2.125 = 3.711072193
x = 3.711072193

Simplifying
x = 3.711072193


Subproblem 2
x + -2.125 = -1.586072193

Simplifying
x + -2.125 = -1.586072193

Reorder the terms:
-2.125 + x = -1.586072193

Solving
-2.125 + x = -1.586072193

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x = -1.586072193 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = -1.586072193 + 2.125
x = -1.586072193 + 2.125

Combine like terms: -1.586072193 + 2.125 = 0.538927807
x = 0.538927807

Simplifying
x = 0.538927807


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.711072193, 0.538927807}

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