x^2+2.5x+1.5=0

Solution for x^2+2.5x+1.5=0 equation:

Simplifying
x2 + 2.5x + 1.5 = 0

Reorder the terms:
1.5 + 2.5x + x2 = 0

Solving
1.5 + 2.5x + 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 + 2.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 2.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 2.5x + x2 = 0 + -1.5
2.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
2.5x + x2 = -1.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = -1.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = -1.5 + 1.5625

Combine like terms: -1.5 + 1.5625 = 0.0625
1.5625 + 2.5x + x2 = 0.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 0.0625

Calculate the square root of the right side: 0.25

Break this problem into two subproblems by setting 
(x + 1.25) equal to 0.25 and -0.25.

Subproblem 1
x + 1.25 = 0.25

Simplifying
x + 1.25 = 0.25

Reorder the terms:
1.25 + x = 0.25

Solving
1.25 + x = 0.25

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 0.25 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 0.25 + -1.25
x = 0.25 + -1.25

Combine like terms: 0.25 + -1.25 = -1
x = -1

Simplifying
x = -1

Subproblem 2
x + 1.25 = -0.25

Simplifying
x + 1.25 = -0.25

Reorder the terms:
1.25 + x = -0.25

Solving
1.25 + x = -0.25

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -0.25 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -0.25 + -1.25
x = -0.25 + -1.25

Combine like terms: -0.25 + -1.25 = -1.5
x = -1.5

Simplifying
x = -1.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1, -1.5}