11x^2-26x+4=0

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Solution for 11x^2-26x+4=0 equation:


Simplifying
11x2 + -26x + 4 = 0

Reorder the terms:
4 + -26x + 11x2 = 0

Solving
4 + -26x + 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'.
0.3636363636 + -2.363636364x + x2 = 0

Move the constant term to the right:

Add '-0.3636363636' to each side of the equation.
0.3636363636 + -2.363636364x + -0.3636363636 + x2 = 0 + -0.3636363636

Reorder the terms:
0.3636363636 + -0.3636363636 + -2.363636364x + x2 = 0 + -0.3636363636

Combine like terms: 0.3636363636 + -0.3636363636 = 0.0000000000
0.0000000000 + -2.363636364x + x2 = 0 + -0.3636363636
-2.363636364x + x2 = 0 + -0.3636363636

Combine like terms: 0 + -0.3636363636 = -0.3636363636
-2.363636364x + x2 = -0.3636363636

The x term is -2.363636364x.  Take half its coefficient (-1.181818182).
Square it (1.396694215) and add it to both sides.

Add '1.396694215' to each side of the equation.
-2.363636364x + 1.396694215 + x2 = -0.3636363636 + 1.396694215

Reorder the terms:
1.396694215 + -2.363636364x + x2 = -0.3636363636 + 1.396694215

Combine like terms: -0.3636363636 + 1.396694215 = 1.0330578514
1.396694215 + -2.363636364x + x2 = 1.0330578514

Factor a perfect square on the left side:
(x + -1.181818182)(x + -1.181818182) = 1.0330578514

Calculate the square root of the right side: 1.016394535

Break this problem into two subproblems by setting 
(x + -1.181818182) equal to 1.016394535 and -1.016394535.

Subproblem 1

x + -1.181818182 = 1.016394535 Simplifying x + -1.181818182 = 1.016394535 Reorder the terms: -1.181818182 + x = 1.016394535 Solving -1.181818182 + x = 1.016394535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.181818182' to each side of the equation. -1.181818182 + 1.181818182 + x = 1.016394535 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + x = 1.016394535 + 1.181818182 x = 1.016394535 + 1.181818182 Combine like terms: 1.016394535 + 1.181818182 = 2.198212717 x = 2.198212717 Simplifying x = 2.198212717

Subproblem 2

x + -1.181818182 = -1.016394535 Simplifying x + -1.181818182 = -1.016394535 Reorder the terms: -1.181818182 + x = -1.016394535 Solving -1.181818182 + x = -1.016394535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.181818182' to each side of the equation. -1.181818182 + 1.181818182 + x = -1.016394535 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + x = -1.016394535 + 1.181818182 x = -1.016394535 + 1.181818182 Combine like terms: -1.016394535 + 1.181818182 = 0.165423647 x = 0.165423647 Simplifying x = 0.165423647

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.198212717, 0.165423647}

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