x^2+6x+9=55

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Solution for x^2+6x+9=55 equation:


Simplifying
x2 + 6x + 9 = 55

Reorder the terms:
9 + 6x + x2 = 55

Solving
9 + 6x + x2 = 55

Solving for variable 'x'.

Reorder the terms:
9 + -55 + 6x + x2 = 55 + -55

Combine like terms: 9 + -55 = -46
-46 + 6x + x2 = 55 + -55

Combine like terms: 55 + -55 = 0
-46 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + 6x + 46 + x2 = 0 + 46

Reorder the terms:
-46 + 46 + 6x + x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 6x + x2 = 0 + 46
6x + x2 = 0 + 46

Combine like terms: 0 + 46 = 46
6x + x2 = 46

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 = 46 + 9

Reorder the terms:
9 + 6x + x2 = 46 + 9

Combine like terms: 46 + 9 = 55
9 + 6x + x2 = 55

Factor a perfect square on the left side:
(x + 3)(x + 3) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + 3) equal to 7.416198487 and -7.416198487.

Subproblem 1

x + 3 = 7.416198487 Simplifying x + 3 = 7.416198487 Reorder the terms: 3 + x = 7.416198487 Solving 3 + x = 7.416198487 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 = 7.416198487 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.416198487 + -3 x = 7.416198487 + -3 Combine like terms: 7.416198487 + -3 = 4.416198487 x = 4.416198487 Simplifying x = 4.416198487

Subproblem 2

x + 3 = -7.416198487 Simplifying x + 3 = -7.416198487 Reorder the terms: 3 + x = -7.416198487 Solving 3 + x = -7.416198487 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 = -7.416198487 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.416198487 + -3 x = -7.416198487 + -3 Combine like terms: -7.416198487 + -3 = -10.416198487 x = -10.416198487 Simplifying x = -10.416198487

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.416198487, -10.416198487}

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