x^2-1.375x+0.375=0

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Solution for x^2-1.375x+0.375=0 equation: 


Simplifying
x2 + -1.375x + 0.375 = 0

Reorder the terms:
0.375 + -1.375x + x2 = 0

Solving
0.375 + -1.375x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -1.375x + -0.375 + x2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -1.375x + x2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -1.375x + x2 = 0 + -0.375
-1.375x + x2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-1.375x + x2 = -0.375

The x term is -1.375x.  Take half its coefficient (-0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
-1.375x + 0.47265625 + x2 = -0.375 + 0.47265625

Reorder the terms:
0.47265625 + -1.375x + x2 = -0.375 + 0.47265625

Combine like terms: -0.375 + 0.47265625 = 0.09765625
0.47265625 + -1.375x + x2 = 0.09765625

Factor a perfect square on the left side:
(x + -0.6875)(x + -0.6875) = 0.09765625

Calculate the square root of the right side: 0.3125

Break this problem into two subproblems by setting 
(x + -0.6875) equal to 0.3125 and -0.3125.


Subproblem 1
x + -0.6875 = 0.3125

Simplifying
x + -0.6875 = 0.3125

Reorder the terms:
-0.6875 + x = 0.3125

Solving
-0.6875 + x = 0.3125

Solving for variable 'x'.

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

Add '0.6875' to each side of the equation.
-0.6875 + 0.6875 + x = 0.3125 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + x = 0.3125 + 0.6875
x = 0.3125 + 0.6875

Combine like terms: 0.3125 + 0.6875 = 1
x = 1

Simplifying
x = 1


Subproblem 2
x + -0.6875 = -0.3125

Simplifying
x + -0.6875 = -0.3125

Reorder the terms:
-0.6875 + x = -0.3125

Solving
-0.6875 + x = -0.3125

Solving for variable 'x'.

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

Add '0.6875' to each side of the equation.
-0.6875 + 0.6875 + x = -0.3125 + 0.6875

Combine like terms: -0.6875 + 0.6875 = 0.0000
0.0000 + x = -0.3125 + 0.6875
x = -0.3125 + 0.6875

Combine like terms: -0.3125 + 0.6875 = 0.375
x = 0.375

Simplifying
x = 0.375


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1, 0.375}

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