5m^2+25m-36=0

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Solution for 5m^2+25m-36=0 equation:


Simplifying
5m2 + 25m + -36 = 0

Reorder the terms:
-36 + 25m + 5m2 = 0

Solving
-36 + 25m + 5m2 = 0

Solving for variable 'm'.

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

Divide each side by '5'.
-7.2 + 5m + m2 = 0

Move the constant term to the right:

Add '7.2' to each side of the equation.
-7.2 + 5m + 7.2 + m2 = 0 + 7.2

Reorder the terms:
-7.2 + 7.2 + 5m + m2 = 0 + 7.2

Combine like terms: -7.2 + 7.2 = 0.0
0.0 + 5m + m2 = 0 + 7.2
5m + m2 = 0 + 7.2

Combine like terms: 0 + 7.2 = 7.2
5m + m2 = 7.2

The m term is 5m.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5m + 6.25 + m2 = 7.2 + 6.25

Reorder the terms:
6.25 + 5m + m2 = 7.2 + 6.25

Combine like terms: 7.2 + 6.25 = 13.45
6.25 + 5m + m2 = 13.45

Factor a perfect square on the left side:
(m + 2.5)(m + 2.5) = 13.45

Calculate the square root of the right side: 3.667424164

Break this problem into two subproblems by setting 
(m + 2.5) equal to 3.667424164 and -3.667424164.

Subproblem 1

m + 2.5 = 3.667424164 Simplifying m + 2.5 = 3.667424164 Reorder the terms: 2.5 + m = 3.667424164 Solving 2.5 + m = 3.667424164 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = 3.667424164 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = 3.667424164 + -2.5 m = 3.667424164 + -2.5 Combine like terms: 3.667424164 + -2.5 = 1.167424164 m = 1.167424164 Simplifying m = 1.167424164

Subproblem 2

m + 2.5 = -3.667424164 Simplifying m + 2.5 = -3.667424164 Reorder the terms: 2.5 + m = -3.667424164 Solving 2.5 + m = -3.667424164 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + m = -3.667424164 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + m = -3.667424164 + -2.5 m = -3.667424164 + -2.5 Combine like terms: -3.667424164 + -2.5 = -6.167424164 m = -6.167424164 Simplifying m = -6.167424164

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.167424164, -6.167424164}

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