2(x)*(x)=-12x-3

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Solution for 2(x)*(x)=-12x-3 equation:


Simplifying
2(x)(x) = -12x + -3

Multiply x * x
2x2 = -12x + -3

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

Solving
2x2 = -3 + -12x

Solving for variable 'x'.

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

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

Combine like terms: -3 + 3 = 0
3 + 12x + 2x2 = 0 + -12x + 12x
3 + 12x + 2x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
3 + 12x + 2x2 = 0

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

Divide each side by '2'.
1.5 + 6x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 6x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 6x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 6x + x2 = 0 + -1.5
6x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
6x + x2 = -1.5

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -1.5 + 9

Reorder the terms:
9 + 6x + x2 = -1.5 + 9

Combine like terms: -1.5 + 9 = 7.5
9 + 6x + x2 = 7.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 7.5

Calculate the square root of the right side: 2.738612788

Break this problem into two subproblems by setting 
(x + 3) equal to 2.738612788 and -2.738612788.

Subproblem 1

x + 3 = 2.738612788 Simplifying x + 3 = 2.738612788 Reorder the terms: 3 + x = 2.738612788 Solving 3 + x = 2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 2.738612788 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.738612788 + -3 x = 2.738612788 + -3 Combine like terms: 2.738612788 + -3 = -0.261387212 x = -0.261387212 Simplifying x = -0.261387212

Subproblem 2

x + 3 = -2.738612788 Simplifying x + 3 = -2.738612788 Reorder the terms: 3 + x = -2.738612788 Solving 3 + x = -2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -2.738612788 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.738612788 + -3 x = -2.738612788 + -3 Combine like terms: -2.738612788 + -3 = -5.738612788 x = -5.738612788 Simplifying x = -5.738612788

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.261387212, -5.738612788}

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