x^2-4x-1.5=0

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Solution for x^2-4x-1.5=0 equation: 


Simplifying
x2 + -4x + -1.5 = 0

Reorder the terms:
-1.5 + -4x + x2 = 0

Solving
-1.5 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -4x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -4x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -4x + x2 = 0 + 1.5
-4x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-4x + x2 = 1.5

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1.5 + 4

Reorder the terms:
4 + -4x + x2 = 1.5 + 4

Combine like terms: 1.5 + 4 = 5.5
4 + -4x + x2 = 5.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(x + -2) equal to 2.34520788 and -2.34520788.


Subproblem 1
x + -2 = 2.34520788

Simplifying
x + -2 = 2.34520788

Reorder the terms:
-2 + x = 2.34520788

Solving
-2 + x = 2.34520788

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.34520788 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.34520788 + 2
x = 2.34520788 + 2

Combine like terms: 2.34520788 + 2 = 4.34520788
x = 4.34520788

Simplifying
x = 4.34520788


Subproblem 2
x + -2 = -2.34520788

Simplifying
x + -2 = -2.34520788

Reorder the terms:
-2 + x = -2.34520788

Solving
-2 + x = -2.34520788

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.34520788 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.34520788 + 2
x = -2.34520788 + 2

Combine like terms: -2.34520788 + 2 = -0.34520788
x = -0.34520788

Simplifying
x = -0.34520788


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.34520788, -0.34520788}

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