x^2+3x-0.5=0

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Solution for x^2+3x-0.5=0 equation: 


Simplifying
x2 + 3x + -0.5 = 0

Reorder the terms:
-0.5 + 3x + x2 = 0

Solving
-0.5 + 3x + 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 + 3x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 3x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 3x + x2 = 0 + 0.5
3x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
3x + x2 = 0.5

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 = 0.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 0.5 + 2.25

Combine like terms: 0.5 + 2.25 = 2.75
2.25 + 3x + x2 = 2.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.658312395 and -1.658312395.


Subproblem 1
x + 1.5 = 1.658312395

Simplifying
x + 1.5 = 1.658312395

Reorder the terms:
1.5 + x = 1.658312395

Solving
1.5 + x = 1.658312395

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 = 1.658312395 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 1.658312395 + -1.5
x = 1.658312395 + -1.5

Combine like terms: 1.658312395 + -1.5 = 0.158312395
x = 0.158312395

Simplifying
x = 0.158312395


Subproblem 2
x + 1.5 = -1.658312395

Simplifying
x + 1.5 = -1.658312395

Reorder the terms:
1.5 + x = -1.658312395

Solving
1.5 + x = -1.658312395

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 = -1.658312395 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -1.658312395 + -1.5
x = -1.658312395 + -1.5

Combine like terms: -1.658312395 + -1.5 = -3.158312395
x = -3.158312395

Simplifying
x = -3.158312395


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.158312395, -3.158312395}

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