(3x^2-12x)-14=0

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Solution for (3x^2-12x)-14=0 equation:


Simplifying
(3x2 + -12x) + -14 = 0

Reorder the terms:
(-12x + 3x2) + -14 = 0

Remove parenthesis around (-12x + 3x2)
-12x + 3x2 + -14 = 0

Reorder the terms:
-14 + -12x + 3x2 = 0

Solving
-14 + -12x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-4.666666667 + -4x + x2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + -4x + 4.666666667 + x2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + -4x + x2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + -4x + x2 = 0 + 4.666666667
-4x + x2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
-4x + x2 = 4.666666667

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 = 4.666666667 + 4

Reorder the terms:
4 + -4x + x2 = 4.666666667 + 4

Combine like terms: 4.666666667 + 4 = 8.666666667
4 + -4x + x2 = 8.666666667

Factor a perfect square on the left side:
(x + -2)(x + -2) = 8.666666667

Calculate the square root of the right side: 2.943920289

Break this problem into two subproblems by setting 
(x + -2) equal to 2.943920289 and -2.943920289.

Subproblem 1

x + -2 = 2.943920289 Simplifying x + -2 = 2.943920289 Reorder the terms: -2 + x = 2.943920289 Solving -2 + x = 2.943920289 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 = 2.943920289 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.943920289 + 2 x = 2.943920289 + 2 Combine like terms: 2.943920289 + 2 = 4.943920289 x = 4.943920289 Simplifying x = 4.943920289

Subproblem 2

x + -2 = -2.943920289 Simplifying x + -2 = -2.943920289 Reorder the terms: -2 + x = -2.943920289 Solving -2 + x = -2.943920289 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 = -2.943920289 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.943920289 + 2 x = -2.943920289 + 2 Combine like terms: -2.943920289 + 2 = -0.943920289 x = -0.943920289 Simplifying x = -0.943920289

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.943920289, -0.943920289}

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