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

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


Simplifying
0 = 0.5x2 + -1.5x + -0.375

Reorder the terms:
0 = -0.375 + -1.5x + 0.5x2

Solving
0 = -0.375 + -1.5x + 0.5x2

Solving for variable 'x'.

Combine like terms: 0 + 0.375 = 0.375
0.375 + 1.5x + -0.5x2 = -0.375 + -1.5x + 0.5x2 + 0.375 + 1.5x + -0.5x2

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

Combine like terms: -0.375 + 0.375 = 0.000
0.375 + 1.5x + -0.5x2 = 0.000 + -1.5x + 1.5x + 0.5x2 + -0.5x2
0.375 + 1.5x + -0.5x2 = -1.5x + 1.5x + 0.5x2 + -0.5x2

Combine like terms: -1.5x + 1.5x = 0.0
0.375 + 1.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2
0.375 + 1.5x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
0.375 + 1.5x + -0.5x2 = 0.0

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

Divide each side by '-0.5'.
-0.75 + -3x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -3x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -3x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -3x + x2 = 0 + 0.75
-3x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-3x + x2 = 0.75

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 0.75 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 0.75 + 2.25

Combine like terms: 0.75 + 2.25 = 3
2.25 + -3x + x2 = 3

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + -1.5 = 1.732050808

Simplifying
x + -1.5 = 1.732050808

Reorder the terms:
-1.5 + x = 1.732050808

Solving
-1.5 + x = 1.732050808

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 1.732050808 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 1.732050808 + 1.5
x = 1.732050808 + 1.5

Combine like terms: 1.732050808 + 1.5 = 3.232050808
x = 3.232050808

Simplifying
x = 3.232050808


Subproblem 2
x + -1.5 = -1.732050808

Simplifying
x + -1.5 = -1.732050808

Reorder the terms:
-1.5 + x = -1.732050808

Solving
-1.5 + x = -1.732050808

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -1.732050808 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -1.732050808 + 1.5
x = -1.732050808 + 1.5

Combine like terms: -1.732050808 + 1.5 = -0.232050808
x = -0.232050808

Simplifying
x = -0.232050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.232050808, -0.232050808}

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