3m^2+5m-4=

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Solution for 3m^2+5m-4= equation: 


Simplifying
3m2 + 5m + -4 = 0

Reorder the terms:
-4 + 5m + 3m2 = 0

Solving
-4 + 5m + 3m2 = 0

Solving for variable 'm'.

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

Divide each side by '3'.
-1.333333333 + 1.666666667m + m2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 1.666666667m + 1.333333333 + m2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 1.666666667m + m2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 1.666666667m + m2 = 0 + 1.333333333
1.666666667m + m2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
1.666666667m + m2 = 1.333333333

The m term is 1.666666667m.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667m + 0.6944444447 + m2 = 1.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667m + m2 = 1.333333333 + 0.6944444447

Combine like terms: 1.333333333 + 0.6944444447 = 2.0277777777
0.6944444447 + 1.666666667m + m2 = 2.0277777777

Factor a perfect square on the left side:
(m + 0.8333333335)(m + 0.8333333335) = 2.0277777777

Calculate the square root of the right side: 1.424000624

Break this problem into two subproblems by setting 
(m + 0.8333333335) equal to 1.424000624 and -1.424000624.


Subproblem 1
m + 0.8333333335 = 1.424000624

Simplifying
m + 0.8333333335 = 1.424000624

Reorder the terms:
0.8333333335 + m = 1.424000624

Solving
0.8333333335 + m = 1.424000624

Solving for variable 'm'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + m = 1.424000624 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + m = 1.424000624 + -0.8333333335
m = 1.424000624 + -0.8333333335

Combine like terms: 1.424000624 + -0.8333333335 = 0.5906672905
m = 0.5906672905

Simplifying
m = 0.5906672905


Subproblem 2
m + 0.8333333335 = -1.424000624

Simplifying
m + 0.8333333335 = -1.424000624

Reorder the terms:
0.8333333335 + m = -1.424000624

Solving
0.8333333335 + m = -1.424000624

Solving for variable 'm'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + m = -1.424000624 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + m = -1.424000624 + -0.8333333335
m = -1.424000624 + -0.8333333335

Combine like terms: -1.424000624 + -0.8333333335 = -2.2573339575
m = -2.2573339575

Simplifying
m = -2.2573339575


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {0.5906672905, -2.2573339575}

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