2x^2+12x+7=0

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Solution for 2x^2+12x+7=0 equation:


Simplifying
2x2 + 12x + 7 = 0

Reorder the terms:
7 + 12x + 2x2 = 0

Solving
7 + 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'.
3.5 + 6x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 6x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 6x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 6x + x2 = 0 + -3.5
6x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
6x + x2 = -3.5

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 = -3.5 + 9

Reorder the terms:
9 + 6x + x2 = -3.5 + 9

Combine like terms: -3.5 + 9 = 5.5
9 + 6x + x2 = 5.5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 5.5

Calculate the square root of the right side: 2.34520788

Break this problem into two subproblems by setting 
(x + 3) equal to 2.34520788 and -2.34520788.

Subproblem 1

x + 3 = 2.34520788 Simplifying x + 3 = 2.34520788 Reorder the terms: 3 + x = 2.34520788 Solving 3 + x = 2.34520788 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 = 2.34520788 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.34520788 + -3 x = 2.34520788 + -3 Combine like terms: 2.34520788 + -3 = -0.65479212 x = -0.65479212 Simplifying x = -0.65479212

Subproblem 2

x + 3 = -2.34520788 Simplifying x + 3 = -2.34520788 Reorder the terms: 3 + x = -2.34520788 Solving 3 + x = -2.34520788 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 = -2.34520788 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.34520788 + -3 x = -2.34520788 + -3 Combine like terms: -2.34520788 + -3 = -5.34520788 x = -5.34520788 Simplifying x = -5.34520788

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.65479212, -5.34520788}

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