3m+6+m^2+5m-1=

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Solution for 3m+6+m^2+5m-1= equation:


Simplifying
3m + 6 + m2 + 5m + -1 = 0

Reorder the terms:
6 + -1 + 3m + 5m + m2 = 0

Combine like terms: 6 + -1 = 5
5 + 3m + 5m + m2 = 0

Combine like terms: 3m + 5m = 8m
5 + 8m + m2 = 0

Solving
5 + 8m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 8m + -5 + m2 = 0 + -5

Reorder the terms:
5 + -5 + 8m + m2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8m + m2 = 0 + -5
8m + m2 = 0 + -5

Combine like terms: 0 + -5 = -5
8m + m2 = -5

The m term is 8m.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8m + 16 + m2 = -5 + 16

Reorder the terms:
16 + 8m + m2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + 8m + m2 = 11

Factor a perfect square on the left side:
(m + 4)(m + 4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(m + 4) equal to 3.31662479 and -3.31662479.

Subproblem 1

m + 4 = 3.31662479 Simplifying m + 4 = 3.31662479 Reorder the terms: 4 + m = 3.31662479 Solving 4 + m = 3.31662479 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m = 3.31662479 + -4 Combine like terms: 4 + -4 = 0 0 + m = 3.31662479 + -4 m = 3.31662479 + -4 Combine like terms: 3.31662479 + -4 = -0.68337521 m = -0.68337521 Simplifying m = -0.68337521

Subproblem 2

m + 4 = -3.31662479 Simplifying m + 4 = -3.31662479 Reorder the terms: 4 + m = -3.31662479 Solving 4 + m = -3.31662479 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + m = -3.31662479 + -4 Combine like terms: 4 + -4 = 0 0 + m = -3.31662479 + -4 m = -3.31662479 + -4 Combine like terms: -3.31662479 + -4 = -7.31662479 m = -7.31662479 Simplifying m = -7.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. m = {-0.68337521, -7.31662479}

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