x^2+4.33x-3.33=0

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Solution for x^2+4.33x-3.33=0 equation:


Simplifying
x2 + 4.33x + -3.33 = 0

Reorder the terms:
-3.33 + 4.33x + x2 = 0

Solving
-3.33 + 4.33x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3.33' to each side of the equation.
-3.33 + 4.33x + 3.33 + x2 = 0 + 3.33

Reorder the terms:
-3.33 + 3.33 + 4.33x + x2 = 0 + 3.33

Combine like terms: -3.33 + 3.33 = 0.00
0.00 + 4.33x + x2 = 0 + 3.33
4.33x + x2 = 0 + 3.33

Combine like terms: 0 + 3.33 = 3.33
4.33x + x2 = 3.33

The x term is 4.33x.  Take half its coefficient (2.165).
Square it (4.687225) and add it to both sides.

Add '4.687225' to each side of the equation.
4.33x + 4.687225 + x2 = 3.33 + 4.687225

Reorder the terms:
4.687225 + 4.33x + x2 = 3.33 + 4.687225

Combine like terms: 3.33 + 4.687225 = 8.017225
4.687225 + 4.33x + x2 = 8.017225

Factor a perfect square on the left side:
(x + 2.165)(x + 2.165) = 8.017225

Calculate the square root of the right side: 2.831470466

Break this problem into two subproblems by setting 
(x + 2.165) equal to 2.831470466 and -2.831470466.


Subproblem 1
x + 2.165 = 2.831470466

Simplifying
x + 2.165 = 2.831470466

Reorder the terms:
2.165 + x = 2.831470466

Solving
2.165 + x = 2.831470466

Solving for variable 'x'.

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

Add '-2.165' to each side of the equation.
2.165 + -2.165 + x = 2.831470466 + -2.165

Combine like terms: 2.165 + -2.165 = 0.000
0.000 + x = 2.831470466 + -2.165
x = 2.831470466 + -2.165

Combine like terms: 2.831470466 + -2.165 = 0.666470466
x = 0.666470466

Simplifying
x = 0.666470466


Subproblem 2
x + 2.165 = -2.831470466

Simplifying
x + 2.165 = -2.831470466

Reorder the terms:
2.165 + x = -2.831470466

Solving
2.165 + x = -2.831470466

Solving for variable 'x'.

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

Add '-2.165' to each side of the equation.
2.165 + -2.165 + x = -2.831470466 + -2.165

Combine like terms: 2.165 + -2.165 = 0.000
0.000 + x = -2.831470466 + -2.165
x = -2.831470466 + -2.165

Combine like terms: -2.831470466 + -2.165 = -4.996470466
x = -4.996470466

Simplifying
x = -4.996470466


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.666470466, -4.996470466}

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