2m^2+17m+22=

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Solution for 2m^2+17m+22= equation:


Simplifying
2m2 + 17m + 22 = 0

Reorder the terms:
22 + 17m + 2m2 = 0

Solving
22 + 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'.
11 + 8.5m + m2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 8.5m + -11 + m2 = 0 + -11

Reorder the terms:
11 + -11 + 8.5m + m2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 8.5m + m2 = 0 + -11
8.5m + m2 = 0 + -11

Combine like terms: 0 + -11 = -11
8.5m + m2 = -11

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 = -11 + 18.0625

Reorder the terms:
18.0625 + 8.5m + m2 = -11 + 18.0625

Combine like terms: -11 + 18.0625 = 7.0625
18.0625 + 8.5m + m2 = 7.0625

Factor a perfect square on the left side:
(m + 4.25)(m + 4.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(m + 4.25) equal to 2.657536453 and -2.657536453.

Subproblem 1

m + 4.25 = 2.657536453 Simplifying m + 4.25 = 2.657536453 Reorder the terms: 4.25 + m = 2.657536453 Solving 4.25 + m = 2.657536453 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 = 2.657536453 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + m = 2.657536453 + -4.25 m = 2.657536453 + -4.25 Combine like terms: 2.657536453 + -4.25 = -1.592463547 m = -1.592463547 Simplifying m = -1.592463547

Subproblem 2

m + 4.25 = -2.657536453 Simplifying m + 4.25 = -2.657536453 Reorder the terms: 4.25 + m = -2.657536453 Solving 4.25 + m = -2.657536453 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 = -2.657536453 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + m = -2.657536453 + -4.25 m = -2.657536453 + -4.25 Combine like terms: -2.657536453 + -4.25 = -6.907536453 m = -6.907536453 Simplifying m = -6.907536453

Solution

The solution to the problem is based on the solutions from the subproblems. m = {-1.592463547, -6.907536453}

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