11x^2+4x-2=0

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Solution for 11x^2+4x-2=0 equation:


Simplifying
11x2 + 4x + -2 = 0

Reorder the terms:
-2 + 4x + 11x2 = 0

Solving
-2 + 4x + 11x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
11 the coefficient of the squared term: 

Divide each side by '11'.
-0.1818181818 + 0.3636363636x + x2 = 0

Move the constant term to the right:

Add '0.1818181818' to each side of the equation.
-0.1818181818 + 0.3636363636x + 0.1818181818 + x2 = 0 + 0.1818181818

Reorder the terms:
-0.1818181818 + 0.1818181818 + 0.3636363636x + x2 = 0 + 0.1818181818

Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000
0.0000000000 + 0.3636363636x + x2 = 0 + 0.1818181818
0.3636363636x + x2 = 0 + 0.1818181818

Combine like terms: 0 + 0.1818181818 = 0.1818181818
0.3636363636x + x2 = 0.1818181818

The x term is 0.3636363636x.  Take half its coefficient (0.1818181818).
Square it (0.03305785123) and add it to both sides.

Add '0.03305785123' to each side of the equation.
0.3636363636x + 0.03305785123 + x2 = 0.1818181818 + 0.03305785123

Reorder the terms:
0.03305785123 + 0.3636363636x + x2 = 0.1818181818 + 0.03305785123

Combine like terms: 0.1818181818 + 0.03305785123 = 0.21487603303
0.03305785123 + 0.3636363636x + x2 = 0.21487603303

Factor a perfect square on the left side:
(x + 0.1818181818)(x + 0.1818181818) = 0.21487603303

Calculate the square root of the right side: 0.463547228

Break this problem into two subproblems by setting 
(x + 0.1818181818) equal to 0.463547228 and -0.463547228.

Subproblem 1

x + 0.1818181818 = 0.463547228 Simplifying x + 0.1818181818 = 0.463547228 Reorder the terms: 0.1818181818 + x = 0.463547228 Solving 0.1818181818 + x = 0.463547228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = 0.463547228 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = 0.463547228 + -0.1818181818 x = 0.463547228 + -0.1818181818 Combine like terms: 0.463547228 + -0.1818181818 = 0.2817290462 x = 0.2817290462 Simplifying x = 0.2817290462

Subproblem 2

x + 0.1818181818 = -0.463547228 Simplifying x + 0.1818181818 = -0.463547228 Reorder the terms: 0.1818181818 + x = -0.463547228 Solving 0.1818181818 + x = -0.463547228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = -0.463547228 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = -0.463547228 + -0.1818181818 x = -0.463547228 + -0.1818181818 Combine like terms: -0.463547228 + -0.1818181818 = -0.6453654098 x = -0.6453654098 Simplifying x = -0.6453654098

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2817290462, -0.6453654098}

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