.24m^2+.22m-.35=0

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Solution for .24m^2+.22m-.35=0 equation: 


Simplifying
0.24m2 + 0.22m + -0.35 = 0

Reorder the terms:
-0.35 + 0.22m + 0.24m2 = 0

Solving
-0.35 + 0.22m + 0.24m2 = 0

Solving for variable 'm'.

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

Divide each side by '0.24'.
-1.458333333 + 0.9166666667m + m2 = 0

Move the constant term to the right:

Add '1.458333333' to each side of the equation.
-1.458333333 + 0.9166666667m + 1.458333333 + m2 = 0 + 1.458333333

Reorder the terms:
-1.458333333 + 1.458333333 + 0.9166666667m + m2 = 0 + 1.458333333

Combine like terms: -1.458333333 + 1.458333333 = 0.000000000
0.000000000 + 0.9166666667m + m2 = 0 + 1.458333333
0.9166666667m + m2 = 0 + 1.458333333

Combine like terms: 0 + 1.458333333 = 1.458333333
0.9166666667m + m2 = 1.458333333

The m term is 0.9166666667m.  Take half its coefficient (0.4583333334).
Square it (0.2100694445) and add it to both sides.

Add '0.2100694445' to each side of the equation.
0.9166666667m + 0.2100694445 + m2 = 1.458333333 + 0.2100694445

Reorder the terms:
0.2100694445 + 0.9166666667m + m2 = 1.458333333 + 0.2100694445

Combine like terms: 1.458333333 + 0.2100694445 = 1.6684027775
0.2100694445 + 0.9166666667m + m2 = 1.6684027775

Factor a perfect square on the left side:
(m + 0.4583333334)(m + 0.4583333334) = 1.6684027775

Calculate the square root of the right side: 1.291666667

Break this problem into two subproblems by setting 
(m + 0.4583333334) equal to 1.291666667 and -1.291666667.


Subproblem 1
m + 0.4583333334 = 1.291666667

Simplifying
m + 0.4583333334 = 1.291666667

Reorder the terms:
0.4583333334 + m = 1.291666667

Solving
0.4583333334 + m = 1.291666667

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-0.4583333334' to each side of the equation.
0.4583333334 + -0.4583333334 + m = 1.291666667 + -0.4583333334

Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000
0.0000000000 + m = 1.291666667 + -0.4583333334
m = 1.291666667 + -0.4583333334

Combine like terms: 1.291666667 + -0.4583333334 = 0.8333333336
m = 0.8333333336

Simplifying
m = 0.8333333336


Subproblem 2
m + 0.4583333334 = -1.291666667

Simplifying
m + 0.4583333334 = -1.291666667

Reorder the terms:
0.4583333334 + m = -1.291666667

Solving
0.4583333334 + m = -1.291666667

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '-0.4583333334' to each side of the equation.
0.4583333334 + -0.4583333334 + m = -1.291666667 + -0.4583333334

Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000
0.0000000000 + m = -1.291666667 + -0.4583333334
m = -1.291666667 + -0.4583333334

Combine like terms: -1.291666667 + -0.4583333334 = -1.7500000004
m = -1.7500000004

Simplifying
m = -1.7500000004


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.8333333336, -1.7500000004}

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