9x^2-12x+4=11

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Solution for 9x^2-12x+4=11 equation:


Simplifying
9x2 + -12x + 4 = 11

Reorder the terms:
4 + -12x + 9x2 = 11

Solving
4 + -12x + 9x2 = 11

Solving for variable 'x'.

Reorder the terms:
4 + -11 + -12x + 9x2 = 11 + -11

Combine like terms: 4 + -11 = -7
-7 + -12x + 9x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-7 + -12x + 9x2 = 0

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

Divide each side by '9'.
-0.7777777778 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.7777777778' to each side of the equation.
-0.7777777778 + -1.333333333x + 0.7777777778 + x2 = 0 + 0.7777777778

Reorder the terms:
-0.7777777778 + 0.7777777778 + -1.333333333x + x2 = 0 + 0.7777777778

Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000
0.0000000000 + -1.333333333x + x2 = 0 + 0.7777777778
-1.333333333x + x2 = 0 + 0.7777777778

Combine like terms: 0 + 0.7777777778 = 0.7777777778
-1.333333333x + x2 = 0.7777777778

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 0.7777777778 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 0.7777777778 + 0.4444444442

Combine like terms: 0.7777777778 + 0.4444444442 = 1.222222222
0.4444444442 + -1.333333333x + x2 = 1.222222222

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 1.222222222

Calculate the square root of the right side: 1.105541597

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 1.105541597 and -1.105541597.

Subproblem 1

x + -0.6666666665 = 1.105541597 Simplifying x + -0.6666666665 = 1.105541597 Reorder the terms: -0.6666666665 + x = 1.105541597 Solving -0.6666666665 + x = 1.105541597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.105541597 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.105541597 + 0.6666666665 x = 1.105541597 + 0.6666666665 Combine like terms: 1.105541597 + 0.6666666665 = 1.7722082635 x = 1.7722082635 Simplifying x = 1.7722082635

Subproblem 2

x + -0.6666666665 = -1.105541597 Simplifying x + -0.6666666665 = -1.105541597 Reorder the terms: -0.6666666665 + x = -1.105541597 Solving -0.6666666665 + x = -1.105541597 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.105541597 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.105541597 + 0.6666666665 x = -1.105541597 + 0.6666666665 Combine like terms: -1.105541597 + 0.6666666665 = -0.4388749305 x = -0.4388749305 Simplifying x = -0.4388749305

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7722082635, -0.4388749305}

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