0.5*x^2-1.5*x-0.375=x

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Solution for 0.5*x^2-1.5*x-0.375=x equation: 


Simplifying
0.5x2 + -1.5x + -0.375 = x

Reorder the terms:
-0.375 + -1.5x + 0.5x2 = x

Solving
-0.375 + -1.5x + 0.5x2 = x

Solving for variable 'x'.

Reorder the terms:
-0.375 + -1.5x + -1x + 0.5x2 = x + -1x

Combine like terms: -1.5x + -1x = -2.5x
-0.375 + -2.5x + 0.5x2 = x + -1x

Combine like terms: x + -1x = 0
-0.375 + -2.5x + 0.5x2 = 0

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

Divide each side by '0.5'.
-0.75 + -5x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -5x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -5x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -5x + x2 = 0 + 0.75
-5x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-5x + x2 = 0.75

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 = 0.75 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 0.75 + 6.25

Combine like terms: 0.75 + 6.25 = 7
6.25 + -5x + x2 = 7

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -2.5) equal to 2.645751311 and -2.645751311.


Subproblem 1
x + -2.5 = 2.645751311

Simplifying
x + -2.5 = 2.645751311

Reorder the terms:
-2.5 + x = 2.645751311

Solving
-2.5 + x = 2.645751311

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 = 2.645751311 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 2.645751311 + 2.5
x = 2.645751311 + 2.5

Combine like terms: 2.645751311 + 2.5 = 5.145751311
x = 5.145751311

Simplifying
x = 5.145751311


Subproblem 2
x + -2.5 = -2.645751311

Simplifying
x + -2.5 = -2.645751311

Reorder the terms:
-2.5 + x = -2.645751311

Solving
-2.5 + x = -2.645751311

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 = -2.645751311 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -2.645751311 + 2.5
x = -2.645751311 + 2.5

Combine like terms: -2.645751311 + 2.5 = -0.145751311
x = -0.145751311

Simplifying
x = -0.145751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.145751311, -0.145751311}

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