m^2-4m-13=0

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Solution for m^2-4m-13=0 equation:


Simplifying
m2 + -4m + -13 = 0

Reorder the terms:
-13 + -4m + m2 = 0

Solving
-13 + -4m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -4m + 13 + m2 = 0 + 13

Reorder the terms:
-13 + 13 + -4m + m2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -4m + m2 = 0 + 13
-4m + m2 = 0 + 13

Combine like terms: 0 + 13 = 13
-4m + m2 = 13

The m term is -4m.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4m + 4 + m2 = 13 + 4

Reorder the terms:
4 + -4m + m2 = 13 + 4

Combine like terms: 13 + 4 = 17
4 + -4m + m2 = 17

Factor a perfect square on the left side:
(m + -2)(m + -2) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(m + -2) equal to 4.123105626 and -4.123105626.

Subproblem 1

m + -2 = 4.123105626 Simplifying m + -2 = 4.123105626 Reorder the terms: -2 + m = 4.123105626 Solving -2 + m = 4.123105626 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + m = 4.123105626 + 2 m = 4.123105626 + 2 Combine like terms: 4.123105626 + 2 = 6.123105626 m = 6.123105626 Simplifying m = 6.123105626

Subproblem 2

m + -2 = -4.123105626 Simplifying m + -2 = -4.123105626 Reorder the terms: -2 + m = -4.123105626 Solving -2 + m = -4.123105626 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + m = -4.123105626 + 2 m = -4.123105626 + 2 Combine like terms: -4.123105626 + 2 = -2.123105626 m = -2.123105626 Simplifying m = -2.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. m = {6.123105626, -2.123105626}

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