9m^2+2m=10

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Solution for 9m^2+2m=10 equation:


Simplifying
9m2 + 2m = 10

Reorder the terms:
2m + 9m2 = 10

Solving
2m + 9m2 = 10

Solving for variable 'm'.

Reorder the terms:
-10 + 2m + 9m2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 2m + 9m2 = 0

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

Divide each side by '9'.
-1.111111111 + 0.2222222222m + m2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + 0.2222222222m + 1.111111111 + m2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + 0.2222222222m + m2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + 0.2222222222m + m2 = 0 + 1.111111111
0.2222222222m + m2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
0.2222222222m + m2 = 1.111111111

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 = 1.111111111 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222m + m2 = 1.111111111 + 0.01234567901

Combine like terms: 1.111111111 + 0.01234567901 = 1.12345679001
0.01234567901 + 0.2222222222m + m2 = 1.12345679001

Factor a perfect square on the left side:
(m + 0.1111111111)(m + 0.1111111111) = 1.12345679001

Calculate the square root of the right side: 1.059932446

Break this problem into two subproblems by setting 
(m + 0.1111111111) equal to 1.059932446 and -1.059932446.

Subproblem 1

m + 0.1111111111 = 1.059932446 Simplifying m + 0.1111111111 = 1.059932446 Reorder the terms: 0.1111111111 + m = 1.059932446 Solving 0.1111111111 + m = 1.059932446 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 = 1.059932446 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + m = 1.059932446 + -0.1111111111 m = 1.059932446 + -0.1111111111 Combine like terms: 1.059932446 + -0.1111111111 = 0.9488213349 m = 0.9488213349 Simplifying m = 0.9488213349

Subproblem 2

m + 0.1111111111 = -1.059932446 Simplifying m + 0.1111111111 = -1.059932446 Reorder the terms: 0.1111111111 + m = -1.059932446 Solving 0.1111111111 + m = -1.059932446 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 = -1.059932446 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + m = -1.059932446 + -0.1111111111 m = -1.059932446 + -0.1111111111 Combine like terms: -1.059932446 + -0.1111111111 = -1.1710435571 m = -1.1710435571 Simplifying m = -1.1710435571

Solution

The solution to the problem is based on the solutions from the subproblems. m = {0.9488213349, -1.1710435571}

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