x^2+2x-.333=0

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Solution for x^2+2x-.333=0 equation:


Simplifying
x2 + 2x + -0.333 = 0

Reorder the terms:
-0.333 + 2x + x2 = 0

Solving
-0.333 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.333' to each side of the equation.
-0.333 + 2x + 0.333 + x2 = 0 + 0.333

Reorder the terms:
-0.333 + 0.333 + 2x + x2 = 0 + 0.333

Combine like terms: -0.333 + 0.333 = 0.000
0.000 + 2x + x2 = 0 + 0.333
2x + x2 = 0 + 0.333

Combine like terms: 0 + 0.333 = 0.333
2x + x2 = 0.333

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 = 0.333 + 1

Reorder the terms:
1 + 2x + x2 = 0.333 + 1

Combine like terms: 0.333 + 1 = 1.333
1 + 2x + x2 = 1.333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.333

Calculate the square root of the right side: 1.154556192

Break this problem into two subproblems by setting 
(x + 1) equal to 1.154556192 and -1.154556192.

Subproblem 1

x + 1 = 1.154556192 Simplifying x + 1 = 1.154556192 Reorder the terms: 1 + x = 1.154556192 Solving 1 + x = 1.154556192 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 = 1.154556192 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.154556192 + -1 x = 1.154556192 + -1 Combine like terms: 1.154556192 + -1 = 0.154556192 x = 0.154556192 Simplifying x = 0.154556192

Subproblem 2

x + 1 = -1.154556192 Simplifying x + 1 = -1.154556192 Reorder the terms: 1 + x = -1.154556192 Solving 1 + x = -1.154556192 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 = -1.154556192 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.154556192 + -1 x = -1.154556192 + -1 Combine like terms: -1.154556192 + -1 = -2.154556192 x = -2.154556192 Simplifying x = -2.154556192

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.154556192, -2.154556192}

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