x^2+6x=130

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Solution for x^2+6x=130 equation:


Simplifying
x2 + 6x = 130

Reorder the terms:
6x + x2 = 130

Solving
6x + x2 = 130

Solving for variable 'x'.

Reorder the terms:
-130 + 6x + x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + 6x + 130 + x2 = 0 + 130

Reorder the terms:
-130 + 130 + 6x + x2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + 6x + x2 = 0 + 130
6x + x2 = 0 + 130

Combine like terms: 0 + 130 = 130
6x + x2 = 130

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 = 130 + 9

Reorder the terms:
9 + 6x + x2 = 130 + 9

Combine like terms: 130 + 9 = 139
9 + 6x + x2 = 139

Factor a perfect square on the left side:
(x + 3)(x + 3) = 139

Calculate the square root of the right side: 11.789826123

Break this problem into two subproblems by setting 
(x + 3) equal to 11.789826123 and -11.789826123.

Subproblem 1

x + 3 = 11.789826123 Simplifying x + 3 = 11.789826123 Reorder the terms: 3 + x = 11.789826123 Solving 3 + x = 11.789826123 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 = 11.789826123 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.789826123 + -3 x = 11.789826123 + -3 Combine like terms: 11.789826123 + -3 = 8.789826123 x = 8.789826123 Simplifying x = 8.789826123

Subproblem 2

x + 3 = -11.789826123 Simplifying x + 3 = -11.789826123 Reorder the terms: 3 + x = -11.789826123 Solving 3 + x = -11.789826123 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 = -11.789826123 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.789826123 + -3 x = -11.789826123 + -3 Combine like terms: -11.789826123 + -3 = -14.789826123 x = -14.789826123 Simplifying x = -14.789826123

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.789826123, -14.789826123}

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