x^2+2x-105=0

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Solution for x^2+2x-105=0 equation: 


Simplifying
x2 + 2x + -105 = 0

Reorder the terms:
-105 + 2x + x2 = 0

Solving
-105 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 2x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + 2x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 2x + x2 = 0 + 105
2x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
2x + x2 = 105

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 = 105 + 1

Reorder the terms:
1 + 2x + x2 = 105 + 1

Combine like terms: 105 + 1 = 106
1 + 2x + x2 = 106

Factor a perfect square on the left side:
(x + 1)(x + 1) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + 1) equal to 10.295630141 and -10.295630141.


Subproblem 1
x + 1 = 10.295630141

Simplifying
x + 1 = 10.295630141

Reorder the terms:
1 + x = 10.295630141

Solving
1 + x = 10.295630141

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 = 10.295630141 + -1

Combine like terms: 1 + -1 = 0
0 + x = 10.295630141 + -1
x = 10.295630141 + -1

Combine like terms: 10.295630141 + -1 = 9.295630141
x = 9.295630141

Simplifying
x = 9.295630141


Subproblem 2
x + 1 = -10.295630141

Simplifying
x + 1 = -10.295630141

Reorder the terms:
1 + x = -10.295630141

Solving
1 + x = -10.295630141

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 = -10.295630141 + -1

Combine like terms: 1 + -1 = 0
0 + x = -10.295630141 + -1
x = -10.295630141 + -1

Combine like terms: -10.295630141 + -1 = -11.295630141
x = -11.295630141

Simplifying
x = -11.295630141


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.295630141, -11.295630141}

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