10m^2-20m-34=4

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Solution for 10m^2-20m-34=4 equation: 


Simplifying
10m2 + -20m + -34 = 4

Reorder the terms:
-34 + -20m + 10m2 = 4

Solving
-34 + -20m + 10m2 = 4

Solving for variable 'm'.

Reorder the terms:
-34 + -4 + -20m + 10m2 = 4 + -4

Combine like terms: -34 + -4 = -38
-38 + -20m + 10m2 = 4 + -4

Combine like terms: 4 + -4 = 0
-38 + -20m + 10m2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + -10m + 5m2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-19 + -10m + 5m2)' equal to zero and attempt to solve:

Simplifying
-19 + -10m + 5m2 = 0

Solving
-19 + -10m + 5m2 = 0

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

Divide each side by '5'.
-3.8 + -2m + m2 = 0

Move the constant term to the right:

Add '3.8' to each side of the equation.
-3.8 + -2m + 3.8 + m2 = 0 + 3.8

Reorder the terms:
-3.8 + 3.8 + -2m + m2 = 0 + 3.8

Combine like terms: -3.8 + 3.8 = 0.0
0.0 + -2m + m2 = 0 + 3.8
-2m + m2 = 0 + 3.8

Combine like terms: 0 + 3.8 = 3.8
-2m + m2 = 3.8

The m term is -2m.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2m + 1 + m2 = 3.8 + 1

Reorder the terms:
1 + -2m + m2 = 3.8 + 1

Combine like terms: 3.8 + 1 = 4.8
1 + -2m + m2 = 4.8

Factor a perfect square on the left side:
(m + -1)(m + -1) = 4.8

Calculate the square root of the right side: 2.19089023

Break this problem into two subproblems by setting 
(m + -1) equal to 2.19089023 and -2.19089023.


Subproblem 1
m + -1 = 2.19089023

Simplifying
m + -1 = 2.19089023

Reorder the terms:
-1 + m = 2.19089023

Solving
-1 + m = 2.19089023

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = 2.19089023 + 1

Combine like terms: -1 + 1 = 0
0 + m = 2.19089023 + 1
m = 2.19089023 + 1

Combine like terms: 2.19089023 + 1 = 3.19089023
m = 3.19089023

Simplifying
m = 3.19089023


Subproblem 2
m + -1 = -2.19089023

Simplifying
m + -1 = -2.19089023

Reorder the terms:
-1 + m = -2.19089023

Solving
-1 + m = -2.19089023

Solving for variable 'm'.

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

Add '1' to each side of the equation.
-1 + 1 + m = -2.19089023 + 1

Combine like terms: -1 + 1 = 0
0 + m = -2.19089023 + 1
m = -2.19089023 + 1

Combine like terms: -2.19089023 + 1 = -1.19089023
m = -1.19089023

Simplifying
m = -1.19089023


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.19089023, -1.19089023}
Solution
m = {3.19089023, -1.19089023}

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