x^2+6x=23

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Solution for x^2+6x=23 equation:


Simplifying
x2 + 6x = 23

Reorder the terms:
6x + x2 = 23

Solving
6x + x2 = 23

Solving for variable 'x'.

Reorder the terms:
-23 + 6x + x2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 6x + 23 + x2 = 0 + 23

Reorder the terms:
-23 + 23 + 6x + x2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 6x + x2 = 0 + 23
6x + x2 = 0 + 23

Combine like terms: 0 + 23 = 23
6x + x2 = 23

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 = 23 + 9

Reorder the terms:
9 + 6x + x2 = 23 + 9

Combine like terms: 23 + 9 = 32
9 + 6x + x2 = 32

Factor a perfect square on the left side:
(x + 3)(x + 3) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + 3) equal to 5.656854249 and -5.656854249.

Subproblem 1

x + 3 = 5.656854249 Simplifying x + 3 = 5.656854249 Reorder the terms: 3 + x = 5.656854249 Solving 3 + x = 5.656854249 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 = 5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.656854249 + -3 x = 5.656854249 + -3 Combine like terms: 5.656854249 + -3 = 2.656854249 x = 2.656854249 Simplifying x = 2.656854249

Subproblem 2

x + 3 = -5.656854249 Simplifying x + 3 = -5.656854249 Reorder the terms: 3 + x = -5.656854249 Solving 3 + x = -5.656854249 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 = -5.656854249 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.656854249 + -3 x = -5.656854249 + -3 Combine like terms: -5.656854249 + -3 = -8.656854249 x = -8.656854249 Simplifying x = -8.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.656854249, -8.656854249}

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