x^2+6x=168

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Solution for x^2+6x=168 equation:


Simplifying
x2 + 6x = 168

Reorder the terms:
6x + x2 = 168

Solving
6x + x2 = 168

Solving for variable 'x'.

Reorder the terms:
-168 + 6x + x2 = 168 + -168

Combine like terms: 168 + -168 = 0
-168 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '168' to each side of the equation.
-168 + 6x + 168 + x2 = 0 + 168

Reorder the terms:
-168 + 168 + 6x + x2 = 0 + 168

Combine like terms: -168 + 168 = 0
0 + 6x + x2 = 0 + 168
6x + x2 = 0 + 168

Combine like terms: 0 + 168 = 168
6x + x2 = 168

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 = 168 + 9

Reorder the terms:
9 + 6x + x2 = 168 + 9

Combine like terms: 168 + 9 = 177
9 + 6x + x2 = 177

Factor a perfect square on the left side:
(x + 3)(x + 3) = 177

Calculate the square root of the right side: 13.304134696

Break this problem into two subproblems by setting 
(x + 3) equal to 13.304134696 and -13.304134696.

Subproblem 1

x + 3 = 13.304134696 Simplifying x + 3 = 13.304134696 Reorder the terms: 3 + x = 13.304134696 Solving 3 + x = 13.304134696 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 = 13.304134696 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.304134696 + -3 x = 13.304134696 + -3 Combine like terms: 13.304134696 + -3 = 10.304134696 x = 10.304134696 Simplifying x = 10.304134696

Subproblem 2

x + 3 = -13.304134696 Simplifying x + 3 = -13.304134696 Reorder the terms: 3 + x = -13.304134696 Solving 3 + x = -13.304134696 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 = -13.304134696 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.304134696 + -3 x = -13.304134696 + -3 Combine like terms: -13.304134696 + -3 = -16.304134696 x = -16.304134696 Simplifying x = -16.304134696

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.304134696, -16.304134696}

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