6+6x+x^2=0

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Solution for 6+6x+x^2=0 equation:


Simplifying
6 + 6x + x2 = 0

Solving
6 + 6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -6 + 9

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

Combine like terms: -6 + 9 = 3
9 + 6x + x2 = 3

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

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 3) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + 3 = 1.732050808 Simplifying x + 3 = 1.732050808 Reorder the terms: 3 + x = 1.732050808 Solving 3 + x = 1.732050808 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 = 1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.732050808 + -3 x = 1.732050808 + -3 Combine like terms: 1.732050808 + -3 = -1.267949192 x = -1.267949192 Simplifying x = -1.267949192

Subproblem 2

x + 3 = -1.732050808 Simplifying x + 3 = -1.732050808 Reorder the terms: 3 + x = -1.732050808 Solving 3 + x = -1.732050808 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 = -1.732050808 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.732050808 + -3 x = -1.732050808 + -3 Combine like terms: -1.732050808 + -3 = -4.732050808 x = -4.732050808 Simplifying x = -4.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.267949192, -4.732050808}

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