m^2+2m-5=0

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


Simplifying
m2 + 2m + -5 = 0

Reorder the terms:
-5 + 2m + m2 = 0

Solving
-5 + 2m + m2 = 0

Solving for variable 'm'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2m + 5 + m2 = 0 + 5

Reorder the terms:
-5 + 5 + 2m + m2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2m + m2 = 0 + 5
2m + m2 = 0 + 5

Combine like terms: 0 + 5 = 5
2m + m2 = 5

The m term is 2m.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2m + 1 + m2 = 5 + 1

Reorder the terms:
1 + 2m + m2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + 2m + m2 = 6

Factor a perfect square on the left side:
(m + 1)(m + 1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(m + 1) equal to 2.449489743 and -2.449489743.

Subproblem 1

m + 1 = 2.449489743 Simplifying m + 1 = 2.449489743 Reorder the terms: 1 + m = 2.449489743 Solving 1 + m = 2.449489743 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + m = 2.449489743 + -1 m = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 m = 1.449489743 Simplifying m = 1.449489743

Subproblem 2

m + 1 = -2.449489743 Simplifying m + 1 = -2.449489743 Reorder the terms: 1 + m = -2.449489743 Solving 1 + m = -2.449489743 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + m = -2.449489743 + -1 m = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 m = -3.449489743 Simplifying m = -3.449489743

Solution

The solution to the problem is based on the solutions from the subproblems. m = {1.449489743, -3.449489743}

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