m^2-34=-6m

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Solution for m^2-34=-6m equation:


Simplifying
m2 + -34 = -6m

Reorder the terms:
-34 + m2 = -6m

Solving
-34 + m2 = -6m

Solving for variable 'm'.

Reorder the terms:
-34 + 6m + m2 = -6m + 6m

Combine like terms: -6m + 6m = 0
-34 + 6m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + 6m + 34 + m2 = 0 + 34

Reorder the terms:
-34 + 34 + 6m + m2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + 6m + m2 = 0 + 34
6m + m2 = 0 + 34

Combine like terms: 0 + 34 = 34
6m + m2 = 34

The m term is 6m.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6m + 9 + m2 = 34 + 9

Reorder the terms:
9 + 6m + m2 = 34 + 9

Combine like terms: 34 + 9 = 43
9 + 6m + m2 = 43

Factor a perfect square on the left side:
(m + 3)(m + 3) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(m + 3) equal to 6.557438524 and -6.557438524.

Subproblem 1

m + 3 = 6.557438524 Simplifying m + 3 = 6.557438524 Reorder the terms: 3 + m = 6.557438524 Solving 3 + m = 6.557438524 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = 6.557438524 + -3 Combine like terms: 3 + -3 = 0 0 + m = 6.557438524 + -3 m = 6.557438524 + -3 Combine like terms: 6.557438524 + -3 = 3.557438524 m = 3.557438524 Simplifying m = 3.557438524

Subproblem 2

m + 3 = -6.557438524 Simplifying m + 3 = -6.557438524 Reorder the terms: 3 + m = -6.557438524 Solving 3 + m = -6.557438524 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = -6.557438524 + -3 Combine like terms: 3 + -3 = 0 0 + m = -6.557438524 + -3 m = -6.557438524 + -3 Combine like terms: -6.557438524 + -3 = -9.557438524 m = -9.557438524 Simplifying m = -9.557438524

Solution

The solution to the problem is based on the solutions from the subproblems. m = {3.557438524, -9.557438524}

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