11x^2-6x=10

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Solution for 11x^2-6x=10 equation:


Simplifying
11x2 + -6x = 10

Reorder the terms:
-6x + 11x2 = 10

Solving
-6x + 11x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -6x + 11x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -6x + 11x2 = 0

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

Divide each side by '11'.
-0.9090909091 + -0.5454545455x + x2 = 0

Move the constant term to the right:

Add '0.9090909091' to each side of the equation.
-0.9090909091 + -0.5454545455x + 0.9090909091 + x2 = 0 + 0.9090909091

Reorder the terms:
-0.9090909091 + 0.9090909091 + -0.5454545455x + x2 = 0 + 0.9090909091

Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000
0.0000000000 + -0.5454545455x + x2 = 0 + 0.9090909091
-0.5454545455x + x2 = 0 + 0.9090909091

Combine like terms: 0 + 0.9090909091 = 0.9090909091
-0.5454545455x + x2 = 0.9090909091

The x term is -0.5454545455x.  Take half its coefficient (-0.2727272728).
Square it (0.07438016533) and add it to both sides.

Add '0.07438016533' to each side of the equation.
-0.5454545455x + 0.07438016533 + x2 = 0.9090909091 + 0.07438016533

Reorder the terms:
0.07438016533 + -0.5454545455x + x2 = 0.9090909091 + 0.07438016533

Combine like terms: 0.9090909091 + 0.07438016533 = 0.98347107443
0.07438016533 + -0.5454545455x + x2 = 0.98347107443

Factor a perfect square on the left side:
(x + -0.2727272728)(x + -0.2727272728) = 0.98347107443

Calculate the square root of the right side: 0.991701101

Break this problem into two subproblems by setting 
(x + -0.2727272728) equal to 0.991701101 and -0.991701101.

Subproblem 1

x + -0.2727272728 = 0.991701101 Simplifying x + -0.2727272728 = 0.991701101 Reorder the terms: -0.2727272728 + x = 0.991701101 Solving -0.2727272728 + x = 0.991701101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = 0.991701101 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = 0.991701101 + 0.2727272728 x = 0.991701101 + 0.2727272728 Combine like terms: 0.991701101 + 0.2727272728 = 1.2644283738 x = 1.2644283738 Simplifying x = 1.2644283738

Subproblem 2

x + -0.2727272728 = -0.991701101 Simplifying x + -0.2727272728 = -0.991701101 Reorder the terms: -0.2727272728 + x = -0.991701101 Solving -0.2727272728 + x = -0.991701101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = -0.991701101 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = -0.991701101 + 0.2727272728 x = -0.991701101 + 0.2727272728 Combine like terms: -0.991701101 + 0.2727272728 = -0.7189738282 x = -0.7189738282 Simplifying x = -0.7189738282

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2644283738, -0.7189738282}

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