x^2+2x+0.25=0

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Solution for x^2+2x+0.25=0 equation:


Simplifying
x2 + 2x + 0.25 = 0

Reorder the terms:
0.25 + 2x + x2 = 0

Solving
0.25 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 2x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 2x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 2x + x2 = 0 + -0.25
2x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
2x + x2 = -0.25

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.25 + 1

Reorder the terms:
1 + 2x + x2 = -0.25 + 1

Combine like terms: -0.25 + 1 = 0.75
1 + 2x + x2 = 0.75

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(x + 1) equal to 0.866025404 and -0.866025404.

Subproblem 1

x + 1 = 0.866025404 Simplifying x + 1 = 0.866025404 Reorder the terms: 1 + x = 0.866025404 Solving 1 + x = 0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.866025404 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.866025404 + -1 x = 0.866025404 + -1 Combine like terms: 0.866025404 + -1 = -0.133974596 x = -0.133974596 Simplifying x = -0.133974596

Subproblem 2

x + 1 = -0.866025404 Simplifying x + 1 = -0.866025404 Reorder the terms: 1 + x = -0.866025404 Solving 1 + x = -0.866025404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.866025404 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.866025404 + -1 x = -0.866025404 + -1 Combine like terms: -0.866025404 + -1 = -1.866025404 x = -1.866025404 Simplifying x = -1.866025404

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.133974596, -1.866025404}

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