6x^2-11=-8x

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Solution for 6x^2-11=-8x equation:


Simplifying
6x2 + -11 = -8x

Reorder the terms:
-11 + 6x2 = -8x

Solving
-11 + 6x2 = -8x

Solving for variable 'x'.

Reorder the terms:
-11 + 8x + 6x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
-11 + 8x + 6x2 = 0

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

Divide each side by '6'.
-1.833333333 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + 1.333333333x + 1.833333333 + x2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + 1.333333333x + x2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + 1.833333333
1.333333333x + x2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
1.333333333x + x2 = 1.833333333

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 = 1.833333333 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 1.833333333 + 0.4444444442

Combine like terms: 1.833333333 + 0.4444444442 = 2.2777777772
0.4444444442 + 1.333333333x + x2 = 2.2777777772

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 2.2777777772

Calculate the square root of the right side: 1.509230856

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.509230856 and -1.509230856.

Subproblem 1

x + 0.6666666665 = 1.509230856 Simplifying x + 0.6666666665 = 1.509230856 Reorder the terms: 0.6666666665 + x = 1.509230856 Solving 0.6666666665 + x = 1.509230856 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 = 1.509230856 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.509230856 + -0.6666666665 x = 1.509230856 + -0.6666666665 Combine like terms: 1.509230856 + -0.6666666665 = 0.8425641895 x = 0.8425641895 Simplifying x = 0.8425641895

Subproblem 2

x + 0.6666666665 = -1.509230856 Simplifying x + 0.6666666665 = -1.509230856 Reorder the terms: 0.6666666665 + x = -1.509230856 Solving 0.6666666665 + x = -1.509230856 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 = -1.509230856 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.509230856 + -0.6666666665 x = -1.509230856 + -0.6666666665 Combine like terms: -1.509230856 + -0.6666666665 = -2.1758975225 x = -2.1758975225 Simplifying x = -2.1758975225

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8425641895, -2.1758975225}

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