3x^2+11=12x

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Solution for 3x^2+11=12x equation:


Simplifying
3x2 + 11 = 12x

Reorder the terms:
11 + 3x2 = 12x

Solving
11 + 3x2 = 12x

Solving for variable 'x'.

Reorder the terms:
11 + -12x + 3x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
11 + -12x + 3x2 = 0

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

Divide each side by '3'.
3.666666667 + -4x + x2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + -4x + -3.666666667 + x2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + -4x + x2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + -4x + x2 = 0 + -3.666666667
-4x + x2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
-4x + x2 = -3.666666667

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 = -3.666666667 + 4

Reorder the terms:
4 + -4x + x2 = -3.666666667 + 4

Combine like terms: -3.666666667 + 4 = 0.333333333
4 + -4x + x2 = 0.333333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 0.333333333

Calculate the square root of the right side: 0.577350269

Break this problem into two subproblems by setting 
(x + -2) equal to 0.577350269 and -0.577350269.

Subproblem 1

x + -2 = 0.577350269 Simplifying x + -2 = 0.577350269 Reorder the terms: -2 + x = 0.577350269 Solving -2 + x = 0.577350269 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 = 0.577350269 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.577350269 + 2 x = 0.577350269 + 2 Combine like terms: 0.577350269 + 2 = 2.577350269 x = 2.577350269 Simplifying x = 2.577350269

Subproblem 2

x + -2 = -0.577350269 Simplifying x + -2 = -0.577350269 Reorder the terms: -2 + x = -0.577350269 Solving -2 + x = -0.577350269 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 = -0.577350269 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.577350269 + 2 x = -0.577350269 + 2 Combine like terms: -0.577350269 + 2 = 1.422649731 x = 1.422649731 Simplifying x = 1.422649731

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.577350269, 1.422649731}

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