11x^2=122x+11

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Solution for 11x^2=122x+11 equation:


Simplifying
11x2 = 122x + 11

Reorder the terms:
11x2 = 11 + 122x

Solving
11x2 = 11 + 122x

Solving for variable 'x'.

Reorder the terms:
-11 + -122x + 11x2 = 11 + 122x + -11 + -122x

Reorder the terms:
-11 + -122x + 11x2 = 11 + -11 + 122x + -122x

Combine like terms: 11 + -11 = 0
-11 + -122x + 11x2 = 0 + 122x + -122x
-11 + -122x + 11x2 = 122x + -122x

Combine like terms: 122x + -122x = 0
-11 + -122x + 11x2 = 0

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

Divide each side by '11'.
-1 + -11.09090909x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -11.09090909x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -11.09090909x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -11.09090909x + x2 = 0 + 1
-11.09090909x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-11.09090909x + x2 = 1

The x term is -11.09090909x.  Take half its coefficient (-5.545454545).
Square it (30.75206611) and add it to both sides.

Add '30.75206611' to each side of the equation.
-11.09090909x + 30.75206611 + x2 = 1 + 30.75206611

Reorder the terms:
30.75206611 + -11.09090909x + x2 = 1 + 30.75206611

Combine like terms: 1 + 30.75206611 = 31.75206611
30.75206611 + -11.09090909x + x2 = 31.75206611

Factor a perfect square on the left side:
(x + -5.545454545)(x + -5.545454545) = 31.75206611

Calculate the square root of the right side: 5.634897169

Break this problem into two subproblems by setting 
(x + -5.545454545) equal to 5.634897169 and -5.634897169.

Subproblem 1

x + -5.545454545 = 5.634897169 Simplifying x + -5.545454545 = 5.634897169 Reorder the terms: -5.545454545 + x = 5.634897169 Solving -5.545454545 + x = 5.634897169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.545454545' to each side of the equation. -5.545454545 + 5.545454545 + x = 5.634897169 + 5.545454545 Combine like terms: -5.545454545 + 5.545454545 = 0.000000000 0.000000000 + x = 5.634897169 + 5.545454545 x = 5.634897169 + 5.545454545 Combine like terms: 5.634897169 + 5.545454545 = 11.180351714 x = 11.180351714 Simplifying x = 11.180351714

Subproblem 2

x + -5.545454545 = -5.634897169 Simplifying x + -5.545454545 = -5.634897169 Reorder the terms: -5.545454545 + x = -5.634897169 Solving -5.545454545 + x = -5.634897169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.545454545' to each side of the equation. -5.545454545 + 5.545454545 + x = -5.634897169 + 5.545454545 Combine like terms: -5.545454545 + 5.545454545 = 0.000000000 0.000000000 + x = -5.634897169 + 5.545454545 x = -5.634897169 + 5.545454545 Combine like terms: -5.634897169 + 5.545454545 = -0.089442624 x = -0.089442624 Simplifying x = -0.089442624

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.180351714, -0.089442624}

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