m^2+m-17=0

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Solution for m^2+m-17=0 equation:


Simplifying
m2 + m + -17 = 0

Reorder the terms:
-17 + m + m2 = 0

Solving
-17 + m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + m + 17 + m2 = 0 + 17

Reorder the terms:
-17 + 17 + m + m2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + m + m2 = 0 + 17
m + m2 = 0 + 17

Combine like terms: 0 + 17 = 17
m + m2 = 17

The m term is m.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
m + 0.25 + m2 = 17 + 0.25

Reorder the terms:
0.25 + m + m2 = 17 + 0.25

Combine like terms: 17 + 0.25 = 17.25
0.25 + m + m2 = 17.25

Factor a perfect square on the left side:
(m + 0.5)(m + 0.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(m + 0.5) equal to 4.153311931 and -4.153311931.

Subproblem 1

m + 0.5 = 4.153311931 Simplifying m + 0.5 = 4.153311931 Reorder the terms: 0.5 + m = 4.153311931 Solving 0.5 + m = 4.153311931 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 4.153311931 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 4.153311931 + -0.5 m = 4.153311931 + -0.5 Combine like terms: 4.153311931 + -0.5 = 3.653311931 m = 3.653311931 Simplifying m = 3.653311931

Subproblem 2

m + 0.5 = -4.153311931 Simplifying m + 0.5 = -4.153311931 Reorder the terms: 0.5 + m = -4.153311931 Solving 0.5 + m = -4.153311931 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -4.153311931 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -4.153311931 + -0.5 m = -4.153311931 + -0.5 Combine like terms: -4.153311931 + -0.5 = -4.653311931 m = -4.653311931 Simplifying m = -4.653311931

Solution

The solution to the problem is based on the solutions from the subproblems. m = {3.653311931, -4.653311931}

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