2x^2=12x+11

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Solution for 2x^2=12x+11 equation:


Simplifying
2x2 = 12x + 11

Reorder the terms:
2x2 = 11 + 12x

Solving
2x2 = 11 + 12x

Solving for variable 'x'.

Reorder the terms:
-11 + -12x + 2x2 = 11 + 12x + -11 + -12x

Reorder the terms:
-11 + -12x + 2x2 = 11 + -11 + 12x + -12x

Combine like terms: 11 + -11 = 0
-11 + -12x + 2x2 = 0 + 12x + -12x
-11 + -12x + 2x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-11 + -12x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + -6x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -6x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -6x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -6x + x2 = 0 + 5.5
-6x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-6x + x2 = 5.5

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 5.5 + 9

Reorder the terms:
9 + -6x + x2 = 5.5 + 9

Combine like terms: 5.5 + 9 = 14.5
9 + -6x + x2 = 14.5

Factor a perfect square on the left side:
(x + -3)(x + -3) = 14.5

Calculate the square root of the right side: 3.807886553

Break this problem into two subproblems by setting 
(x + -3) equal to 3.807886553 and -3.807886553.

Subproblem 1

x + -3 = 3.807886553 Simplifying x + -3 = 3.807886553 Reorder the terms: -3 + x = 3.807886553 Solving -3 + x = 3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.807886553 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.807886553 + 3 x = 3.807886553 + 3 Combine like terms: 3.807886553 + 3 = 6.807886553 x = 6.807886553 Simplifying x = 6.807886553

Subproblem 2

x + -3 = -3.807886553 Simplifying x + -3 = -3.807886553 Reorder the terms: -3 + x = -3.807886553 Solving -3 + x = -3.807886553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.807886553 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.807886553 + 3 x = -3.807886553 + 3 Combine like terms: -3.807886553 + 3 = -0.807886553 x = -0.807886553 Simplifying x = -0.807886553

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.807886553, -0.807886553}

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