4m^2-17m-12=0

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Solution for 4m^2-17m-12=0 equation: 


Simplifying
4m2 + -17m + -12 = 0

Reorder the terms:
-12 + -17m + 4m2 = 0

Solving
-12 + -17m + 4m2 = 0

Solving for variable 'm'.

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

Divide each side by '4'.
-3 + -4.25m + m2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4.25m + 3 + m2 = 0 + 3

Reorder the terms:
-3 + 3 + -4.25m + m2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4.25m + m2 = 0 + 3
-4.25m + m2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4.25m + m2 = 3

The m term is -4.25m.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25m + 4.515625 + m2 = 3 + 4.515625

Reorder the terms:
4.515625 + -4.25m + m2 = 3 + 4.515625

Combine like terms: 3 + 4.515625 = 7.515625
4.515625 + -4.25m + m2 = 7.515625

Factor a perfect square on the left side:
(m + -2.125)(m + -2.125) = 7.515625

Calculate the square root of the right side: 2.741464025

Break this problem into two subproblems by setting 
(m + -2.125) equal to 2.741464025 and -2.741464025.


Subproblem 1
m + -2.125 = 2.741464025

Simplifying
m + -2.125 = 2.741464025

Reorder the terms:
-2.125 + m = 2.741464025

Solving
-2.125 + m = 2.741464025

Solving for variable 'm'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + m = 2.741464025 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + m = 2.741464025 + 2.125
m = 2.741464025 + 2.125

Combine like terms: 2.741464025 + 2.125 = 4.866464025
m = 4.866464025

Simplifying
m = 4.866464025


Subproblem 2
m + -2.125 = -2.741464025

Simplifying
m + -2.125 = -2.741464025

Reorder the terms:
-2.125 + m = -2.741464025

Solving
-2.125 + m = -2.741464025

Solving for variable 'm'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + m = -2.741464025 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + m = -2.741464025 + 2.125
m = -2.741464025 + 2.125

Combine like terms: -2.741464025 + 2.125 = -0.616464025
m = -0.616464025

Simplifying
m = -0.616464025


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {4.866464025, -0.616464025}

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