x^2+6x=180

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Solution for x^2+6x=180 equation:


Simplifying
x2 + 6x = 180

Reorder the terms:
6x + x2 = 180

Solving
6x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 6x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 6x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + 6x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + 6x + x2 = 0 + 180
6x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
6x + x2 = 180

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 = 180 + 9

Reorder the terms:
9 + 6x + x2 = 180 + 9

Combine like terms: 180 + 9 = 189
9 + 6x + x2 = 189

Factor a perfect square on the left side:
(x + 3)(x + 3) = 189

Calculate the square root of the right side: 13.747727085

Break this problem into two subproblems by setting 
(x + 3) equal to 13.747727085 and -13.747727085.

Subproblem 1

x + 3 = 13.747727085 Simplifying x + 3 = 13.747727085 Reorder the terms: 3 + x = 13.747727085 Solving 3 + x = 13.747727085 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 = 13.747727085 + -3 Combine like terms: 3 + -3 = 0 0 + x = 13.747727085 + -3 x = 13.747727085 + -3 Combine like terms: 13.747727085 + -3 = 10.747727085 x = 10.747727085 Simplifying x = 10.747727085

Subproblem 2

x + 3 = -13.747727085 Simplifying x + 3 = -13.747727085 Reorder the terms: 3 + x = -13.747727085 Solving 3 + x = -13.747727085 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 = -13.747727085 + -3 Combine like terms: 3 + -3 = 0 0 + x = -13.747727085 + -3 x = -13.747727085 + -3 Combine like terms: -13.747727085 + -3 = -16.747727085 x = -16.747727085 Simplifying x = -16.747727085

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.747727085, -16.747727085}

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