2x^2+12x+13=0

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Solution for 2x^2+12x+13=0 equation:


Simplifying
2x2 + 12x + 13 = 0

Reorder the terms:
13 + 12x + 2x2 = 0

Solving
13 + 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'.
6.5 + 6x + x2 = 0

Move the constant term to the right:

Add '-6.5' to each side of the equation.
6.5 + 6x + -6.5 + x2 = 0 + -6.5

Reorder the terms:
6.5 + -6.5 + 6x + x2 = 0 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + 6x + x2 = 0 + -6.5
6x + x2 = 0 + -6.5

Combine like terms: 0 + -6.5 = -6.5
6x + x2 = -6.5

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 = -6.5 + 9

Reorder the terms:
9 + 6x + x2 = -6.5 + 9

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

Factor a perfect square on the left side:
(x + 3)(x + 3) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + 3) equal to 1.58113883 and -1.58113883.

Subproblem 1

x + 3 = 1.58113883 Simplifying x + 3 = 1.58113883 Reorder the terms: 3 + x = 1.58113883 Solving 3 + x = 1.58113883 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 = 1.58113883 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.58113883 + -3 x = 1.58113883 + -3 Combine like terms: 1.58113883 + -3 = -1.41886117 x = -1.41886117 Simplifying x = -1.41886117

Subproblem 2

x + 3 = -1.58113883 Simplifying x + 3 = -1.58113883 Reorder the terms: 3 + x = -1.58113883 Solving 3 + x = -1.58113883 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 = -1.58113883 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.58113883 + -3 x = -1.58113883 + -3 Combine like terms: -1.58113883 + -3 = -4.58113883 x = -4.58113883 Simplifying x = -4.58113883

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.41886117, -4.58113883}

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