9m^2+2m-16=0

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Solution for 9m^2+2m-16=0 equation:


Simplifying
9m2 + 2m + -16 = 0

Reorder the terms:
-16 + 2m + 9m2 = 0

Solving
-16 + 2m + 9m2 = 0

Solving for variable 'm'.

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

Divide each side by '9'.
-1.777777778 + 0.2222222222m + m2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + 0.2222222222m + 1.777777778 + m2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + 0.2222222222m + m2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + 0.2222222222m + m2 = 0 + 1.777777778
0.2222222222m + m2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
0.2222222222m + m2 = 1.777777778

The m term is 0.2222222222m.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222m + 0.01234567901 + m2 = 1.777777778 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222m + m2 = 1.777777778 + 0.01234567901

Combine like terms: 1.777777778 + 0.01234567901 = 1.79012345701
0.01234567901 + 0.2222222222m + m2 = 1.79012345701

Factor a perfect square on the left side:
(m + 0.1111111111)(m + 0.1111111111) = 1.79012345701

Calculate the square root of the right side: 1.337954953

Break this problem into two subproblems by setting 
(m + 0.1111111111) equal to 1.337954953 and -1.337954953.

Subproblem 1

m + 0.1111111111 = 1.337954953 Simplifying m + 0.1111111111 = 1.337954953 Reorder the terms: 0.1111111111 + m = 1.337954953 Solving 0.1111111111 + m = 1.337954953 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + m = 1.337954953 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + m = 1.337954953 + -0.1111111111 m = 1.337954953 + -0.1111111111 Combine like terms: 1.337954953 + -0.1111111111 = 1.2268438419 m = 1.2268438419 Simplifying m = 1.2268438419

Subproblem 2

m + 0.1111111111 = -1.337954953 Simplifying m + 0.1111111111 = -1.337954953 Reorder the terms: 0.1111111111 + m = -1.337954953 Solving 0.1111111111 + m = -1.337954953 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + m = -1.337954953 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + m = -1.337954953 + -0.1111111111 m = -1.337954953 + -0.1111111111 Combine like terms: -1.337954953 + -0.1111111111 = -1.4490660641 m = -1.4490660641 Simplifying m = -1.4490660641

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.2268438419, -1.4490660641}

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