x^2-180+12x-6=0

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Solution for x^2-180+12x-6=0 equation:


Simplifying
x2 + -180 + 12x + -6 = 0

Reorder the terms:
-180 + -6 + 12x + x2 = 0

Combine like terms: -180 + -6 = -186
-186 + 12x + x2 = 0

Solving
-186 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '186' to each side of the equation.
-186 + 12x + 186 + x2 = 0 + 186

Reorder the terms:
-186 + 186 + 12x + x2 = 0 + 186

Combine like terms: -186 + 186 = 0
0 + 12x + x2 = 0 + 186
12x + x2 = 0 + 186

Combine like terms: 0 + 186 = 186
12x + x2 = 186

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 186 + 36

Reorder the terms:
36 + 12x + x2 = 186 + 36

Combine like terms: 186 + 36 = 222
36 + 12x + x2 = 222

Factor a perfect square on the left side:
(x + 6)(x + 6) = 222

Calculate the square root of the right side: 14.899664426

Break this problem into two subproblems by setting 
(x + 6) equal to 14.899664426 and -14.899664426.

Subproblem 1

x + 6 = 14.899664426 Simplifying x + 6 = 14.899664426 Reorder the terms: 6 + x = 14.899664426 Solving 6 + x = 14.899664426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 14.899664426 + -6 Combine like terms: 6 + -6 = 0 0 + x = 14.899664426 + -6 x = 14.899664426 + -6 Combine like terms: 14.899664426 + -6 = 8.899664426 x = 8.899664426 Simplifying x = 8.899664426

Subproblem 2

x + 6 = -14.899664426 Simplifying x + 6 = -14.899664426 Reorder the terms: 6 + x = -14.899664426 Solving 6 + x = -14.899664426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -14.899664426 + -6 Combine like terms: 6 + -6 = 0 0 + x = -14.899664426 + -6 x = -14.899664426 + -6 Combine like terms: -14.899664426 + -6 = -20.899664426 x = -20.899664426 Simplifying x = -20.899664426

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.899664426, -20.899664426}

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