7x^2+39x+12=0

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Solution for 7x^2+39x+12=0 equation:


Simplifying
7x2 + 39x + 12 = 0

Reorder the terms:
12 + 39x + 7x2 = 0

Solving
12 + 39x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
1.714285714 + 5.571428571x + x2 = 0

Move the constant term to the right:

Add '-1.714285714' to each side of the equation.
1.714285714 + 5.571428571x + -1.714285714 + x2 = 0 + -1.714285714

Reorder the terms:
1.714285714 + -1.714285714 + 5.571428571x + x2 = 0 + -1.714285714

Combine like terms: 1.714285714 + -1.714285714 = 0.000000000
0.000000000 + 5.571428571x + x2 = 0 + -1.714285714
5.571428571x + x2 = 0 + -1.714285714

Combine like terms: 0 + -1.714285714 = -1.714285714
5.571428571x + x2 = -1.714285714

The x term is 5.571428571x.  Take half its coefficient (2.785714286).
Square it (7.760204083) and add it to both sides.

Add '7.760204083' to each side of the equation.
5.571428571x + 7.760204083 + x2 = -1.714285714 + 7.760204083

Reorder the terms:
7.760204083 + 5.571428571x + x2 = -1.714285714 + 7.760204083

Combine like terms: -1.714285714 + 7.760204083 = 6.045918369
7.760204083 + 5.571428571x + x2 = 6.045918369

Factor a perfect square on the left side:
(x + 2.785714286)(x + 2.785714286) = 6.045918369

Calculate the square root of the right side: 2.458844926

Break this problem into two subproblems by setting 
(x + 2.785714286) equal to 2.458844926 and -2.458844926.

Subproblem 1

x + 2.785714286 = 2.458844926 Simplifying x + 2.785714286 = 2.458844926 Reorder the terms: 2.785714286 + x = 2.458844926 Solving 2.785714286 + x = 2.458844926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.785714286' to each side of the equation. 2.785714286 + -2.785714286 + x = 2.458844926 + -2.785714286 Combine like terms: 2.785714286 + -2.785714286 = 0.000000000 0.000000000 + x = 2.458844926 + -2.785714286 x = 2.458844926 + -2.785714286 Combine like terms: 2.458844926 + -2.785714286 = -0.32686936 x = -0.32686936 Simplifying x = -0.32686936

Subproblem 2

x + 2.785714286 = -2.458844926 Simplifying x + 2.785714286 = -2.458844926 Reorder the terms: 2.785714286 + x = -2.458844926 Solving 2.785714286 + x = -2.458844926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.785714286' to each side of the equation. 2.785714286 + -2.785714286 + x = -2.458844926 + -2.785714286 Combine like terms: 2.785714286 + -2.785714286 = 0.000000000 0.000000000 + x = -2.458844926 + -2.785714286 x = -2.458844926 + -2.785714286 Combine like terms: -2.458844926 + -2.785714286 = -5.244559212 x = -5.244559212 Simplifying x = -5.244559212

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.32686936, -5.244559212}

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