x^2+12x+36=46

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Solution for x^2+12x+36=46 equation:


Simplifying
x2 + 12x + 36 = 46

Reorder the terms:
36 + 12x + x2 = 46

Solving
36 + 12x + x2 = 46

Solving for variable 'x'.

Reorder the terms:
36 + -46 + 12x + x2 = 46 + -46

Combine like terms: 36 + -46 = -10
-10 + 12x + x2 = 46 + -46

Combine like terms: 46 + -46 = 0
-10 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 12x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 12x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 12x + x2 = 0 + 10
12x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
12x + x2 = 10

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 = 10 + 36

Reorder the terms:
36 + 12x + x2 = 10 + 36

Combine like terms: 10 + 36 = 46
36 + 12x + x2 = 46

Factor a perfect square on the left side:
(x + 6)(x + 6) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(x + 6) equal to 6.782329983 and -6.782329983.

Subproblem 1

x + 6 = 6.782329983 Simplifying x + 6 = 6.782329983 Reorder the terms: 6 + x = 6.782329983 Solving 6 + x = 6.782329983 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 = 6.782329983 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.782329983 + -6 x = 6.782329983 + -6 Combine like terms: 6.782329983 + -6 = 0.782329983 x = 0.782329983 Simplifying x = 0.782329983

Subproblem 2

x + 6 = -6.782329983 Simplifying x + 6 = -6.782329983 Reorder the terms: 6 + x = -6.782329983 Solving 6 + x = -6.782329983 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 = -6.782329983 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.782329983 + -6 x = -6.782329983 + -6 Combine like terms: -6.782329983 + -6 = -12.782329983 x = -12.782329983 Simplifying x = -12.782329983

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.782329983, -12.782329983}

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