m^2-8m-25=0

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Solution for m^2-8m-25=0 equation:


Simplifying
m2 + -8m + -25 = 0

Reorder the terms:
-25 + -8m + m2 = 0

Solving
-25 + -8m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -8m + 25 + m2 = 0 + 25

Reorder the terms:
-25 + 25 + -8m + m2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -8m + m2 = 0 + 25
-8m + m2 = 0 + 25

Combine like terms: 0 + 25 = 25
-8m + m2 = 25

The m term is -8m.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8m + 16 + m2 = 25 + 16

Reorder the terms:
16 + -8m + m2 = 25 + 16

Combine like terms: 25 + 16 = 41
16 + -8m + m2 = 41

Factor a perfect square on the left side:
(m + -4)(m + -4) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(m + -4) equal to 6.403124237 and -6.403124237.

Subproblem 1

m + -4 = 6.403124237 Simplifying m + -4 = 6.403124237 Reorder the terms: -4 + m = 6.403124237 Solving -4 + m = 6.403124237 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 6.403124237 + 4 Combine like terms: -4 + 4 = 0 0 + m = 6.403124237 + 4 m = 6.403124237 + 4 Combine like terms: 6.403124237 + 4 = 10.403124237 m = 10.403124237 Simplifying m = 10.403124237

Subproblem 2

m + -4 = -6.403124237 Simplifying m + -4 = -6.403124237 Reorder the terms: -4 + m = -6.403124237 Solving -4 + m = -6.403124237 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -6.403124237 + 4 Combine like terms: -4 + 4 = 0 0 + m = -6.403124237 + 4 m = -6.403124237 + 4 Combine like terms: -6.403124237 + 4 = -2.403124237 m = -2.403124237 Simplifying m = -2.403124237

Solution

The solution to the problem is based on the solutions from the subproblems. m = {10.403124237, -2.403124237}

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