x^2=-6x-4

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Solution for x^2=-6x-4 equation:


Simplifying
x2 = -6x + -4

Reorder the terms:
x2 = -4 + -6x

Solving
x2 = -4 + -6x

Solving for variable 'x'.

Reorder the terms:
4 + 6x + x2 = -4 + -6x + 4 + 6x

Reorder the terms:
4 + 6x + x2 = -4 + 4 + -6x + 6x

Combine like terms: -4 + 4 = 0
4 + 6x + x2 = 0 + -6x + 6x
4 + 6x + x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
4 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 6x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 6x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 6x + x2 = 0 + -4
6x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
6x + x2 = -4

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 = -4 + 9

Reorder the terms:
9 + 6x + x2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + 6x + x2 = 5

Factor a perfect square on the left side:
(x + 3)(x + 3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 3) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + 3 = 2.236067978 Simplifying x + 3 = 2.236067978 Reorder the terms: 3 + x = 2.236067978 Solving 3 + x = 2.236067978 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 = 2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.236067978 + -3 x = 2.236067978 + -3 Combine like terms: 2.236067978 + -3 = -0.763932022 x = -0.763932022 Simplifying x = -0.763932022

Subproblem 2

x + 3 = -2.236067978 Simplifying x + 3 = -2.236067978 Reorder the terms: 3 + x = -2.236067978 Solving 3 + x = -2.236067978 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 = -2.236067978 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.236067978 + -3 x = -2.236067978 + -3 Combine like terms: -2.236067978 + -3 = -5.236067978 x = -5.236067978 Simplifying x = -5.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.763932022, -5.236067978}

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