x^2+6x-105=0

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Solution for x^2+6x-105=0 equation:


Simplifying
x2 + 6x + -105 = 0

Reorder the terms:
-105 + 6x + x2 = 0

Solving
-105 + 6x + 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 + 6x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + 6x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 6x + x2 = 0 + 105
6x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
6x + x2 = 105

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 105 + 9

Reorder the terms:
9 + 6x + x2 = 105 + 9

Combine like terms: 105 + 9 = 114
9 + 6x + x2 = 114

Factor a perfect square on the left side:
(x + 3)(x + 3) = 114

Calculate the square root of the right side: 10.677078252

Break this problem into two subproblems by setting 
(x + 3) equal to 10.677078252 and -10.677078252.

Subproblem 1

x + 3 = 10.677078252 Simplifying x + 3 = 10.677078252 Reorder the terms: 3 + x = 10.677078252 Solving 3 + x = 10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 10.677078252 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.677078252 + -3 x = 10.677078252 + -3 Combine like terms: 10.677078252 + -3 = 7.677078252 x = 7.677078252 Simplifying x = 7.677078252

Subproblem 2

x + 3 = -10.677078252 Simplifying x + 3 = -10.677078252 Reorder the terms: 3 + x = -10.677078252 Solving 3 + x = -10.677078252 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -10.677078252 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.677078252 + -3 x = -10.677078252 + -3 Combine like terms: -10.677078252 + -3 = -13.677078252 x = -13.677078252 Simplifying x = -13.677078252

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.677078252, -13.677078252}

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