x^2-.75x+.140625=1.890625

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Solution for x^2-.75x+.140625=1.890625 equation: 


Simplifying
x2 + -0.75x + 0.140625 = 1.890625

Reorder the terms:
0.140625 + -0.75x + x2 = 1.890625

Solving
0.140625 + -0.75x + x2 = 1.890625

Solving for variable 'x'.

Reorder the terms:
0.140625 + -1.890625 + -0.75x + x2 = 1.890625 + -1.890625

Combine like terms: 0.140625 + -1.890625 = -1.75
-1.75 + -0.75x + x2 = 1.890625 + -1.890625

Combine like terms: 1.890625 + -1.890625 = 0.000000
-1.75 + -0.75x + x2 = 0.000000

Begin completing the square.

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + -0.75x + 1.75 + x2 = 0.000000 + 1.75

Reorder the terms:
-1.75 + 1.75 + -0.75x + x2 = 0.000000 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + -0.75x + x2 = 0.000000 + 1.75
-0.75x + x2 = 0.000000 + 1.75

Combine like terms: 0.000000 + 1.75 = 1.75
-0.75x + x2 = 1.75

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 1.75 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 1.75 + 0.140625

Combine like terms: 1.75 + 0.140625 = 1.890625
0.140625 + -0.75x + x2 = 1.890625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 1.890625

Calculate the square root of the right side: 1.375

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.375 and -1.375.


Subproblem 1
x + -0.375 = 1.375

Simplifying
x + -0.375 = 1.375

Reorder the terms:
-0.375 + x = 1.375

Solving
-0.375 + x = 1.375

Solving for variable 'x'.

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

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

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

Combine like terms: 1.375 + 0.375 = 1.75
x = 1.75

Simplifying
x = 1.75


Subproblem 2
x + -0.375 = -1.375

Simplifying
x + -0.375 = -1.375

Reorder the terms:
-0.375 + x = -1.375

Solving
-0.375 + x = -1.375

Solving for variable 'x'.

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

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

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

Combine like terms: -1.375 + 0.375 = -1
x = -1

Simplifying
x = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.75, -1}

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