11x^2-44x+34=0

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Solution for 11x^2-44x+34=0 equation:


Simplifying
11x2 + -44x + 34 = 0

Reorder the terms:
34 + -44x + 11x2 = 0

Solving
34 + -44x + 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'.
3.090909091 + -4x + x2 = 0

Move the constant term to the right:

Add '-3.090909091' to each side of the equation.
3.090909091 + -4x + -3.090909091 + x2 = 0 + -3.090909091

Reorder the terms:
3.090909091 + -3.090909091 + -4x + x2 = 0 + -3.090909091

Combine like terms: 3.090909091 + -3.090909091 = 0.000000000
0.000000000 + -4x + x2 = 0 + -3.090909091
-4x + x2 = 0 + -3.090909091

Combine like terms: 0 + -3.090909091 = -3.090909091
-4x + x2 = -3.090909091

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -3.090909091 + 4

Reorder the terms:
4 + -4x + x2 = -3.090909091 + 4

Combine like terms: -3.090909091 + 4 = 0.909090909
4 + -4x + x2 = 0.909090909

Factor a perfect square on the left side:
(x + -2)(x + -2) = 0.909090909

Calculate the square root of the right side: 0.953462589

Break this problem into two subproblems by setting 
(x + -2) equal to 0.953462589 and -0.953462589.

Subproblem 1

x + -2 = 0.953462589 Simplifying x + -2 = 0.953462589 Reorder the terms: -2 + x = 0.953462589 Solving -2 + x = 0.953462589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.953462589 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.953462589 + 2 x = 0.953462589 + 2 Combine like terms: 0.953462589 + 2 = 2.953462589 x = 2.953462589 Simplifying x = 2.953462589

Subproblem 2

x + -2 = -0.953462589 Simplifying x + -2 = -0.953462589 Reorder the terms: -2 + x = -0.953462589 Solving -2 + x = -0.953462589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.953462589 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.953462589 + 2 x = -0.953462589 + 2 Combine like terms: -0.953462589 + 2 = 1.046537411 x = 1.046537411 Simplifying x = 1.046537411

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.953462589, 1.046537411}

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