2m^2+13m+14=0

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Solution for 2m^2+13m+14=0 equation:


Simplifying
2m2 + 13m + 14 = 0

Reorder the terms:
14 + 13m + 2m2 = 0

Solving
14 + 13m + 2m2 = 0

Solving for variable 'm'.

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

Divide each side by '2'.
7 + 6.5m + m2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 6.5m + -7 + m2 = 0 + -7

Reorder the terms:
7 + -7 + 6.5m + m2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6.5m + m2 = 0 + -7
6.5m + m2 = 0 + -7

Combine like terms: 0 + -7 = -7
6.5m + m2 = -7

The m term is 6.5m.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5m + 10.5625 + m2 = -7 + 10.5625

Reorder the terms:
10.5625 + 6.5m + m2 = -7 + 10.5625

Combine like terms: -7 + 10.5625 = 3.5625
10.5625 + 6.5m + m2 = 3.5625

Factor a perfect square on the left side:
(m + 3.25)(m + 3.25) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(m + 3.25) equal to 1.887458609 and -1.887458609.

Subproblem 1

m + 3.25 = 1.887458609 Simplifying m + 3.25 = 1.887458609 Reorder the terms: 3.25 + m = 1.887458609 Solving 3.25 + m = 1.887458609 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + m = 1.887458609 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + m = 1.887458609 + -3.25 m = 1.887458609 + -3.25 Combine like terms: 1.887458609 + -3.25 = -1.362541391 m = -1.362541391 Simplifying m = -1.362541391

Subproblem 2

m + 3.25 = -1.887458609 Simplifying m + 3.25 = -1.887458609 Reorder the terms: 3.25 + m = -1.887458609 Solving 3.25 + m = -1.887458609 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + m = -1.887458609 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + m = -1.887458609 + -3.25 m = -1.887458609 + -3.25 Combine like terms: -1.887458609 + -3.25 = -5.137458609 m = -5.137458609 Simplifying m = -5.137458609

Solution

The solution to the problem is based on the solutions from the subproblems. m = {-1.362541391, -5.137458609}

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