x^2-4x+1.25=0

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Solution for x^2-4x+1.25=0 equation: 


Simplifying
x2 + -4x + 1.25 = 0

Reorder the terms:
1.25 + -4x + x2 = 0

Solving
1.25 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -4x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -4x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -4x + x2 = 0 + -1.25
-4x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-4x + x2 = -1.25

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -1.25 + 4

Reorder the terms:
4 + -4x + x2 = -1.25 + 4

Combine like terms: -1.25 + 4 = 2.75
4 + -4x + x2 = 2.75

Factor a perfect square on the left side:
(x + -2)(x + -2) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + -2) equal to 1.658312395 and -1.658312395.


Subproblem 1
x + -2 = 1.658312395

Simplifying
x + -2 = 1.658312395

Reorder the terms:
-2 + x = 1.658312395

Solving
-2 + x = 1.658312395

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 1.658312395 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.658312395 + 2
x = 1.658312395 + 2

Combine like terms: 1.658312395 + 2 = 3.658312395
x = 3.658312395

Simplifying
x = 3.658312395


Subproblem 2
x + -2 = -1.658312395

Simplifying
x + -2 = -1.658312395

Reorder the terms:
-2 + x = -1.658312395

Solving
-2 + x = -1.658312395

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -1.658312395 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.658312395 + 2
x = -1.658312395 + 2

Combine like terms: -1.658312395 + 2 = 0.341687605
x = 0.341687605

Simplifying
x = 0.341687605


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.658312395, 0.341687605}

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