x^2-1.5x-1.44=0

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Solution for x^2-1.5x-1.44=0 equation: 


Simplifying
x2 + -1.5x + -1.44 = 0

Reorder the terms:
-1.44 + -1.5x + x2 = 0

Solving
-1.44 + -1.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1.44' to each side of the equation.
-1.44 + -1.5x + 1.44 + x2 = 0 + 1.44

Reorder the terms:
-1.44 + 1.44 + -1.5x + x2 = 0 + 1.44

Combine like terms: -1.44 + 1.44 = 0.00
0.00 + -1.5x + x2 = 0 + 1.44
-1.5x + x2 = 0 + 1.44

Combine like terms: 0 + 1.44 = 1.44
-1.5x + x2 = 1.44

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 = 1.44 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 1.44 + 0.5625

Combine like terms: 1.44 + 0.5625 = 2.0025
0.5625 + -1.5x + x2 = 2.0025

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 2.0025

Calculate the square root of the right side: 1.41509717

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.41509717 and -1.41509717.


Subproblem 1
x + -0.75 = 1.41509717

Simplifying
x + -0.75 = 1.41509717

Reorder the terms:
-0.75 + x = 1.41509717

Solving
-0.75 + x = 1.41509717

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 = 1.41509717 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.41509717 + 0.75
x = 1.41509717 + 0.75

Combine like terms: 1.41509717 + 0.75 = 2.16509717
x = 2.16509717

Simplifying
x = 2.16509717


Subproblem 2
x + -0.75 = -1.41509717

Simplifying
x + -0.75 = -1.41509717

Reorder the terms:
-0.75 + x = -1.41509717

Solving
-0.75 + x = -1.41509717

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 = -1.41509717 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.41509717 + 0.75
x = -1.41509717 + 0.75

Combine like terms: -1.41509717 + 0.75 = -0.66509717
x = -0.66509717

Simplifying
x = -0.66509717


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.16509717, -0.66509717}

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