3x^2-12=2x+8-6x^2-16

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Solution for 3x^2-12=2x+8-6x^2-16 equation:


Simplifying
3x2 + -12 = 2x + 8 + -6x2 + -16

Reorder the terms:
-12 + 3x2 = 2x + 8 + -6x2 + -16

Reorder the terms:
-12 + 3x2 = 8 + -16 + 2x + -6x2

Combine like terms: 8 + -16 = -8
-12 + 3x2 = -8 + 2x + -6x2

Solving
-12 + 3x2 = -8 + 2x + -6x2

Solving for variable 'x'.

Reorder the terms:
-12 + 8 + -2x + 3x2 + 6x2 = -8 + 2x + -6x2 + 8 + -2x + 6x2

Combine like terms: -12 + 8 = -4
-4 + -2x + 3x2 + 6x2 = -8 + 2x + -6x2 + 8 + -2x + 6x2

Combine like terms: 3x2 + 6x2 = 9x2
-4 + -2x + 9x2 = -8 + 2x + -6x2 + 8 + -2x + 6x2

Reorder the terms:
-4 + -2x + 9x2 = -8 + 8 + 2x + -2x + -6x2 + 6x2

Combine like terms: -8 + 8 = 0
-4 + -2x + 9x2 = 0 + 2x + -2x + -6x2 + 6x2
-4 + -2x + 9x2 = 2x + -2x + -6x2 + 6x2

Combine like terms: 2x + -2x = 0
-4 + -2x + 9x2 = 0 + -6x2 + 6x2
-4 + -2x + 9x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-4 + -2x + 9x2 = 0

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

Divide each side by '9'.
-0.4444444444 + -0.2222222222x + x2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -0.2222222222x + 0.4444444444 + x2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -0.2222222222x + x2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -0.2222222222x + x2 = 0 + 0.4444444444
-0.2222222222x + x2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-0.2222222222x + x2 = 0.4444444444

The x term is -0.2222222222x.  Take half its coefficient (-0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
-0.2222222222x + 0.01234567901 + x2 = 0.4444444444 + 0.01234567901

Reorder the terms:
0.01234567901 + -0.2222222222x + x2 = 0.4444444444 + 0.01234567901

Combine like terms: 0.4444444444 + 0.01234567901 = 0.45679012341
0.01234567901 + -0.2222222222x + x2 = 0.45679012341

Factor a perfect square on the left side:
(x + -0.1111111111)(x + -0.1111111111) = 0.45679012341

Calculate the square root of the right side: 0.675862503

Break this problem into two subproblems by setting 
(x + -0.1111111111) equal to 0.675862503 and -0.675862503.

Subproblem 1

x + -0.1111111111 = 0.675862503 Simplifying x + -0.1111111111 = 0.675862503 Reorder the terms: -0.1111111111 + x = 0.675862503 Solving -0.1111111111 + x = 0.675862503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = 0.675862503 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 0.675862503 + 0.1111111111 x = 0.675862503 + 0.1111111111 Combine like terms: 0.675862503 + 0.1111111111 = 0.7869736141 x = 0.7869736141 Simplifying x = 0.7869736141

Subproblem 2

x + -0.1111111111 = -0.675862503 Simplifying x + -0.1111111111 = -0.675862503 Reorder the terms: -0.1111111111 + x = -0.675862503 Solving -0.1111111111 + x = -0.675862503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = -0.675862503 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -0.675862503 + 0.1111111111 x = -0.675862503 + 0.1111111111 Combine like terms: -0.675862503 + 0.1111111111 = -0.5647513919 x = -0.5647513919 Simplifying x = -0.5647513919

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7869736141, -0.5647513919}

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