35m^2+m-16=0

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Solution for 35m^2+m-16=0 equation:


Simplifying
35m2 + m + -16 = 0

Reorder the terms:
-16 + m + 35m2 = 0

Solving
-16 + m + 35m2 = 0

Solving for variable 'm'.

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

Divide each side by '35'.
-0.4571428571 + 0.02857142857m + m2 = 0

Move the constant term to the right:

Add '0.4571428571' to each side of the equation.
-0.4571428571 + 0.02857142857m + 0.4571428571 + m2 = 0 + 0.4571428571

Reorder the terms:
-0.4571428571 + 0.4571428571 + 0.02857142857m + m2 = 0 + 0.4571428571

Combine like terms: -0.4571428571 + 0.4571428571 = 0.0000000000
0.0000000000 + 0.02857142857m + m2 = 0 + 0.4571428571
0.02857142857m + m2 = 0 + 0.4571428571

Combine like terms: 0 + 0.4571428571 = 0.4571428571
0.02857142857m + m2 = 0.4571428571

The m term is m.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.02857142857m + 0.25 + m2 = 0.4571428571 + 0.25

Reorder the terms:
0.25 + 0.02857142857m + m2 = 0.4571428571 + 0.25

Combine like terms: 0.4571428571 + 0.25 = 0.7071428571
0.25 + 0.02857142857m + m2 = 0.7071428571

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 0.7071428571

Calculate the square root of the right side: 0.840917866

Break this problem into two subproblems by setting 
(m + 0.5) equal to 0.840917866 and -0.840917866.

Subproblem 1

m + 0.5 = 0.840917866 Simplifying m + 0.5 = 0.840917866 Reorder the terms: 0.5 + m = 0.840917866 Solving 0.5 + m = 0.840917866 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 0.840917866 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 0.840917866 + -0.5 m = 0.840917866 + -0.5 Combine like terms: 0.840917866 + -0.5 = 0.340917866 m = 0.340917866 Simplifying m = 0.340917866

Subproblem 2

m + 0.5 = -0.840917866 Simplifying m + 0.5 = -0.840917866 Reorder the terms: 0.5 + m = -0.840917866 Solving 0.5 + m = -0.840917866 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -0.840917866 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -0.840917866 + -0.5 m = -0.840917866 + -0.5 Combine like terms: -0.840917866 + -0.5 = -1.340917866 m = -1.340917866 Simplifying m = -1.340917866

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.340917866, -1.340917866}

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