2x^2+12x+5=0

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Solution for 2x^2+12x+5=0 equation:


Simplifying
2x2 + 12x + 5 = 0

Reorder the terms:
5 + 12x + 2x2 = 0

Solving
5 + 12x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
2.5 + 6x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 6x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 6x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 6x + x2 = 0 + -2.5
6x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
6x + x2 = -2.5

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 = -2.5 + 9

Reorder the terms:
9 + 6x + x2 = -2.5 + 9

Combine like terms: -2.5 + 9 = 6.5
9 + 6x + x2 = 6.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(x + 3) equal to 2.549509757 and -2.549509757.

Subproblem 1

x + 3 = 2.549509757 Simplifying x + 3 = 2.549509757 Reorder the terms: 3 + x = 2.549509757 Solving 3 + x = 2.549509757 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 = 2.549509757 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.549509757 + -3 x = 2.549509757 + -3 Combine like terms: 2.549509757 + -3 = -0.450490243 x = -0.450490243 Simplifying x = -0.450490243

Subproblem 2

x + 3 = -2.549509757 Simplifying x + 3 = -2.549509757 Reorder the terms: 3 + x = -2.549509757 Solving 3 + x = -2.549509757 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 = -2.549509757 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.549509757 + -3 x = -2.549509757 + -3 Combine like terms: -2.549509757 + -3 = -5.549509757 x = -5.549509757 Simplifying x = -5.549509757

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.450490243, -5.549509757}

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