6m^2-2m-4+10m^2+3m-6=

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Solution for 6m^2-2m-4+10m^2+3m-6= equation:


Simplifying
6m2 + -2m + -4 + 10m2 + 3m + -6 = 0

Reorder the terms:
-4 + -6 + -2m + 3m + 6m2 + 10m2 = 0

Combine like terms: -4 + -6 = -10
-10 + -2m + 3m + 6m2 + 10m2 = 0

Combine like terms: -2m + 3m = 1m
-10 + 1m + 6m2 + 10m2 = 0

Combine like terms: 6m2 + 10m2 = 16m2
-10 + 1m + 16m2 = 0

Solving
-10 + 1m + 16m2 = 0

Solving for variable 'm'.

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

Divide each side by '16'.
-0.625 + 0.0625m + m2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 0.0625m + 0.625 + m2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 0.0625m + m2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 0.0625m + m2 = 0 + 0.625
0.0625m + m2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
0.0625m + m2 = 0.625

The m term is 0.0625m.  Take half its coefficient (0.03125).
Square it (0.0009765625) and add it to both sides.

Add '0.0009765625' to each side of the equation.
0.0625m + 0.0009765625 + m2 = 0.625 + 0.0009765625

Reorder the terms:
0.0009765625 + 0.0625m + m2 = 0.625 + 0.0009765625

Combine like terms: 0.625 + 0.0009765625 = 0.6259765625
0.0009765625 + 0.0625m + m2 = 0.6259765625

Factor a perfect square on the left side:
(m + 0.03125)(m + 0.03125) = 0.6259765625

Calculate the square root of the right side: 0.791186806

Break this problem into two subproblems by setting 
(m + 0.03125) equal to 0.791186806 and -0.791186806.

Subproblem 1

m + 0.03125 = 0.791186806 Simplifying m + 0.03125 = 0.791186806 Reorder the terms: 0.03125 + m = 0.791186806 Solving 0.03125 + m = 0.791186806 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + m = 0.791186806 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + m = 0.791186806 + -0.03125 m = 0.791186806 + -0.03125 Combine like terms: 0.791186806 + -0.03125 = 0.759936806 m = 0.759936806 Simplifying m = 0.759936806

Subproblem 2

m + 0.03125 = -0.791186806 Simplifying m + 0.03125 = -0.791186806 Reorder the terms: 0.03125 + m = -0.791186806 Solving 0.03125 + m = -0.791186806 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + m = -0.791186806 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + m = -0.791186806 + -0.03125 m = -0.791186806 + -0.03125 Combine like terms: -0.791186806 + -0.03125 = -0.822436806 m = -0.822436806 Simplifying m = -0.822436806

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.759936806, -0.822436806}

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