x^2+1.5x+0.5=0

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Solution for x^2+1.5x+0.5=0 equation: 


Simplifying
x2 + 1.5x + 0.5 = 0

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

Solving
0.5 + 1.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 1.5x + -0.5 + x2 = 0 + -0.5

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

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 1.5x + x2 = 0 + -0.5
1.5x + x2 = 0 + -0.5

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

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 = -0.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -0.5 + 0.5625

Combine like terms: -0.5 + 0.5625 = 0.0625
0.5625 + 1.5x + x2 = 0.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.0625

Calculate the square root of the right side: 0.25

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.25 and -0.25.


Subproblem 1
x + 0.75 = 0.25

Simplifying
x + 0.75 = 0.25

Reorder the terms:
0.75 + x = 0.25

Solving
0.75 + x = 0.25

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 = 0.25 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 0.25 + -0.75
x = 0.25 + -0.75

Combine like terms: 0.25 + -0.75 = -0.5
x = -0.5

Simplifying
x = -0.5


Subproblem 2
x + 0.75 = -0.25

Simplifying
x + 0.75 = -0.25

Reorder the terms:
0.75 + x = -0.25

Solving
0.75 + x = -0.25

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 = -0.25 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -0.25 + -0.75
x = -0.25 + -0.75

Combine like terms: -0.25 + -0.75 = -1
x = -1

Simplifying
x = -1


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -1}

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