x^2+2.5x-3=0.5

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Solution for x^2+2.5x-3=0.5 equation: 


Simplifying
x2 + 2.5x + -3 = 0.5

Reorder the terms:
-3 + 2.5x + x2 = 0.5

Solving
-3 + 2.5x + x2 = 0.5

Solving for variable 'x'.

Reorder the terms:
-3 + -0.5 + 2.5x + x2 = 0.5 + -0.5

Combine like terms: -3 + -0.5 = -3.5
-3.5 + 2.5x + x2 = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
-3.5 + 2.5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 2.5x + 3.5 + x2 = 0.0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 2.5x + x2 = 0.0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 2.5x + x2 = 0.0 + 3.5
2.5x + x2 = 0.0 + 3.5

Combine like terms: 0.0 + 3.5 = 3.5
2.5x + x2 = 3.5

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 = 3.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 3.5 + 1.5625

Combine like terms: 3.5 + 1.5625 = 5.0625
1.5625 + 2.5x + x2 = 5.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 5.0625

Calculate the square root of the right side: 2.25

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.25 and -2.25.


Subproblem 1
x + 1.25 = 2.25

Simplifying
x + 1.25 = 2.25

Reorder the terms:
1.25 + x = 2.25

Solving
1.25 + x = 2.25

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 = 2.25 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 2.25 + -1.25
x = 2.25 + -1.25

Combine like terms: 2.25 + -1.25 = 1
x = 1

Simplifying
x = 1


Subproblem 2
x + 1.25 = -2.25

Simplifying
x + 1.25 = -2.25

Reorder the terms:
1.25 + x = -2.25

Solving
1.25 + x = -2.25

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 = -2.25 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -2.25 + -1.25
x = -2.25 + -1.25

Combine like terms: -2.25 + -1.25 = -3.5
x = -3.5

Simplifying
x = -3.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1, -3.5}

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