X^2+2X-5=

Solution for X^2+2X-5= equation:

Simplifying
X2 + 2X + -5 = 0

Reorder the terms:
-5 + 2X + X2 = 0

Solving
-5 + 2X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2X + 5 + X2 = 0 + 5

Reorder the terms:
-5 + 5 + 2X + X2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2X + X2 = 0 + 5
2X + X2 = 0 + 5

Combine like terms: 0 + 5 = 5
2X + X2 = 5

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

Add '1' to each side of the equation.
2X + 1 + X2 = 5 + 1

Reorder the terms:
1 + 2X + X2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + 2X + X2 = 6

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

Calculate the square root of the right side: 2.449489743

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

Subproblem 1
X + 1 = 2.449489743

Simplifying
X + 1 = 2.449489743

Reorder the terms:
1 + X = 2.449489743

Solving
1 + X = 2.449489743

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + X = 2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + X = 2.449489743 + -1
X = 2.449489743 + -1

Combine like terms: 2.449489743 + -1 = 1.449489743
X = 1.449489743

Simplifying
X = 1.449489743

Subproblem 2
X + 1 = -2.449489743

Simplifying
X + 1 = -2.449489743

Reorder the terms:
1 + X = -2.449489743

Solving
1 + X = -2.449489743

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + X = -2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + X = -2.449489743 + -1
X = -2.449489743 + -1

Combine like terms: -2.449489743 + -1 = -3.449489743
X = -3.449489743

Simplifying
X = -3.449489743

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