x^2-1.5x-1=0

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Solution for x^2-1.5x-1=0 equation: 


Simplifying
x2 + -1.5x + -1 = 0

Reorder the terms:
-1 + -1.5x + x2 = 0

Solving
-1 + -1.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.5x + x2 = 0 + 1
-1.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.5x + x2 = 1

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 1 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 1 + 0.5625

Combine like terms: 1 + 0.5625 = 1.5625
0.5625 + -1.5x + x2 = 1.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 1.5625

Calculate the square root of the right side: 1.25

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.25 and -1.25.


Subproblem 1
x + -0.75 = 1.25

Simplifying
x + -0.75 = 1.25

Reorder the terms:
-0.75 + x = 1.25

Solving
-0.75 + x = 1.25

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 1.25 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.25 + 0.75
x = 1.25 + 0.75

Combine like terms: 1.25 + 0.75 = 2
x = 2

Simplifying
x = 2


Subproblem 2
x + -0.75 = -1.25

Simplifying
x + -0.75 = -1.25

Reorder the terms:
-0.75 + x = -1.25

Solving
-0.75 + x = -1.25

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -1.25 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.25 + 0.75
x = -1.25 + 0.75

Combine like terms: -1.25 + 0.75 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2, -0.5}

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