2m^2+17m+14=

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Solution for 2m^2+17m+14= equation:


Simplifying
2m2 + 17m + 14 = 0

Reorder the terms:
14 + 17m + 2m2 = 0

Solving
14 + 17m + 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 + 8.5m + m2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 8.5m + -7 + m2 = 0 + -7

Reorder the terms:
7 + -7 + 8.5m + m2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 8.5m + m2 = 0 + -7
8.5m + m2 = 0 + -7

Combine like terms: 0 + -7 = -7
8.5m + m2 = -7

The m term is 8.5m.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5m + 18.0625 + m2 = -7 + 18.0625

Reorder the terms:
18.0625 + 8.5m + m2 = -7 + 18.0625

Combine like terms: -7 + 18.0625 = 11.0625
18.0625 + 8.5m + m2 = 11.0625

Factor a perfect square on the left side:
(m + 4.25)(m + 4.25) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(m + 4.25) equal to 3.326033674 and -3.326033674.

Subproblem 1

m + 4.25 = 3.326033674 Simplifying m + 4.25 = 3.326033674 Reorder the terms: 4.25 + m = 3.326033674 Solving 4.25 + m = 3.326033674 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + m = 3.326033674 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + m = 3.326033674 + -4.25 m = 3.326033674 + -4.25 Combine like terms: 3.326033674 + -4.25 = -0.923966326 m = -0.923966326 Simplifying m = -0.923966326

Subproblem 2

m + 4.25 = -3.326033674 Simplifying m + 4.25 = -3.326033674 Reorder the terms: 4.25 + m = -3.326033674 Solving 4.25 + m = -3.326033674 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + m = -3.326033674 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + m = -3.326033674 + -4.25 m = -3.326033674 + -4.25 Combine like terms: -3.326033674 + -4.25 = -7.576033674 m = -7.576033674 Simplifying m = -7.576033674

Solution

The solution to the problem is based on the solutions from the subproblems. m = {-0.923966326, -7.576033674}

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