x^2+2x-54=0

Solution for x^2+2x-54=0 equation:

Simplifying
x2 + 2x + -54 = 0

Reorder the terms:
-54 + 2x + x2 = 0

Solving
-54 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 2x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 2x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 2x + x2 = 0 + 54
2x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
2x + x2 = 54

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 = 54 + 1

Reorder the terms:
1 + 2x + x2 = 54 + 1

Combine like terms: 54 + 1 = 55
1 + 2x + x2 = 55

Factor a perfect square on the left side:
(x + 1)(x + 1) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + 1) equal to 7.416198487 and -7.416198487.

Subproblem 1
x + 1 = 7.416198487

Simplifying
x + 1 = 7.416198487

Reorder the terms:
1 + x = 7.416198487

Solving
1 + x = 7.416198487

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 = 7.416198487 + -1

Combine like terms: 1 + -1 = 0
0 + x = 7.416198487 + -1
x = 7.416198487 + -1

Combine like terms: 7.416198487 + -1 = 6.416198487
x = 6.416198487

Simplifying
x = 6.416198487

Subproblem 2
x + 1 = -7.416198487

Simplifying
x + 1 = -7.416198487

Reorder the terms:
1 + x = -7.416198487

Solving
1 + x = -7.416198487

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 = -7.416198487 + -1

Combine like terms: 1 + -1 = 0
0 + x = -7.416198487 + -1
x = -7.416198487 + -1

Combine like terms: -7.416198487 + -1 = -8.416198487
x = -8.416198487

Simplifying
x = -8.416198487

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.416198487, -8.416198487}