6x+x^2=121

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Solution for 6x+x^2=121 equation:


Simplifying
6x + x2 = 121

Solving
6x + x2 = 121

Solving for variable 'x'.

Reorder the terms:
-121 + 6x + x2 = 121 + -121

Combine like terms: 121 + -121 = 0
-121 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '121' to each side of the equation.
-121 + 6x + 121 + x2 = 0 + 121

Reorder the terms:
-121 + 121 + 6x + x2 = 0 + 121

Combine like terms: -121 + 121 = 0
0 + 6x + x2 = 0 + 121
6x + x2 = 0 + 121

Combine like terms: 0 + 121 = 121
6x + x2 = 121

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 = 121 + 9

Reorder the terms:
9 + 6x + x2 = 121 + 9

Combine like terms: 121 + 9 = 130
9 + 6x + x2 = 130

Factor a perfect square on the left side:
(x + 3)(x + 3) = 130

Calculate the square root of the right side: 11.401754251

Break this problem into two subproblems by setting 
(x + 3) equal to 11.401754251 and -11.401754251.

Subproblem 1

x + 3 = 11.401754251 Simplifying x + 3 = 11.401754251 Reorder the terms: 3 + x = 11.401754251 Solving 3 + x = 11.401754251 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 = 11.401754251 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11.401754251 + -3 x = 11.401754251 + -3 Combine like terms: 11.401754251 + -3 = 8.401754251 x = 8.401754251 Simplifying x = 8.401754251

Subproblem 2

x + 3 = -11.401754251 Simplifying x + 3 = -11.401754251 Reorder the terms: 3 + x = -11.401754251 Solving 3 + x = -11.401754251 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 = -11.401754251 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11.401754251 + -3 x = -11.401754251 + -3 Combine like terms: -11.401754251 + -3 = -14.401754251 x = -14.401754251 Simplifying x = -14.401754251

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.401754251, -14.401754251}

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