5m(2m-7)=-5

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Solution for 5m(2m-7)=-5 equation:


Simplifying
5m(2m + -7) = -5

Reorder the terms:
5m(-7 + 2m) = -5
(-7 * 5m + 2m * 5m) = -5
(-35m + 10m2) = -5

Solving
-35m + 10m2 = -5

Solving for variable 'm'.

Reorder the terms:
5 + -35m + 10m2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + -35m + 10m2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + -7m + 2m2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(1 + -7m + 2m2)' equal to zero and attempt to solve:

Simplifying
1 + -7m + 2m2 = 0

Solving
1 + -7m + 2m2 = 0

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

Divide each side by '2'.
0.5 + -3.5m + m2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -3.5m + -0.5 + m2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -3.5m + m2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -3.5m + m2 = 0 + -0.5
-3.5m + m2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-3.5m + m2 = -0.5

The m term is -3.5m.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5m + 3.0625 + m2 = -0.5 + 3.0625

Reorder the terms:
3.0625 + -3.5m + m2 = -0.5 + 3.0625

Combine like terms: -0.5 + 3.0625 = 2.5625
3.0625 + -3.5m + m2 = 2.5625

Factor a perfect square on the left side:
(m + -1.75)(m + -1.75) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(m + -1.75) equal to 1.600781059 and -1.600781059.


Subproblem 1
m + -1.75 = 1.600781059

Simplifying
m + -1.75 = 1.600781059

Reorder the terms:
-1.75 + m = 1.600781059

Solving
-1.75 + m = 1.600781059

Solving for variable 'm'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + m = 1.600781059 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + m = 1.600781059 + 1.75
m = 1.600781059 + 1.75

Combine like terms: 1.600781059 + 1.75 = 3.350781059
m = 3.350781059

Simplifying
m = 3.350781059


Subproblem 2
m + -1.75 = -1.600781059

Simplifying
m + -1.75 = -1.600781059

Reorder the terms:
-1.75 + m = -1.600781059

Solving
-1.75 + m = -1.600781059

Solving for variable 'm'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + m = -1.600781059 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + m = -1.600781059 + 1.75
m = -1.600781059 + 1.75

Combine like terms: -1.600781059 + 1.75 = 0.149218941
m = 0.149218941

Simplifying
m = 0.149218941


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {3.350781059, 0.149218941}
Solution
m = {3.350781059, 0.149218941}

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