x^2+0.5x-2.5=0

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Solution for x^2+0.5x-2.5=0 equation: 


Simplifying
x2 + 0.5x + -2.5 = 0

Reorder the terms:
-2.5 + 0.5x + x2 = 0

Solving
-2.5 + 0.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 0.5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 0.5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 0.5x + x2 = 0 + 2.5
0.5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
0.5x + x2 = 2.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 2.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 2.5 + 0.0625

Combine like terms: 2.5 + 0.0625 = 2.5625
0.0625 + 0.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.600781059 and -1.600781059.


Subproblem 1
x + 0.25 = 1.600781059

Simplifying
x + 0.25 = 1.600781059

Reorder the terms:
0.25 + x = 1.600781059

Solving
0.25 + x = 1.600781059

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.600781059 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.600781059 + -0.25
x = 1.600781059 + -0.25

Combine like terms: 1.600781059 + -0.25 = 1.350781059
x = 1.350781059

Simplifying
x = 1.350781059


Subproblem 2
x + 0.25 = -1.600781059

Simplifying
x + 0.25 = -1.600781059

Reorder the terms:
0.25 + x = -1.600781059

Solving
0.25 + x = -1.600781059

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.600781059 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.600781059 + -0.25
x = -1.600781059 + -0.25

Combine like terms: -1.600781059 + -0.25 = -1.850781059
x = -1.850781059

Simplifying
x = -1.850781059


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.350781059, -1.850781059}

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