w^2+6w=-2

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Solution for w^2+6w=-2 equation:


Simplifying
w2 + 6w = -2

Reorder the terms:
6w + w2 = -2

Solving
6w + w2 = -2

Solving for variable 'w'.

Reorder the terms:
2 + 6w + w2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 6w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 6w + -2 + w2 = 0 + -2

Reorder the terms:
2 + -2 + 6w + w2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 6w + w2 = 0 + -2
6w + w2 = 0 + -2

Combine like terms: 0 + -2 = -2
6w + w2 = -2

The w term is 6w.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6w + 9 + w2 = -2 + 9

Reorder the terms:
9 + 6w + w2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + 6w + w2 = 7

Factor a perfect square on the left side:
(w + 3)(w + 3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(w + 3) equal to 2.645751311 and -2.645751311.

Subproblem 1

w + 3 = 2.645751311 Simplifying w + 3 = 2.645751311 Reorder the terms: 3 + w = 2.645751311 Solving 3 + w = 2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + w = 2.645751311 + -3 w = 2.645751311 + -3 Combine like terms: 2.645751311 + -3 = -0.354248689 w = -0.354248689 Simplifying w = -0.354248689

Subproblem 2

w + 3 = -2.645751311 Simplifying w + 3 = -2.645751311 Reorder the terms: 3 + w = -2.645751311 Solving 3 + w = -2.645751311 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -2.645751311 + -3 Combine like terms: 3 + -3 = 0 0 + w = -2.645751311 + -3 w = -2.645751311 + -3 Combine like terms: -2.645751311 + -3 = -5.645751311 w = -5.645751311 Simplifying w = -5.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. w = {-0.354248689, -5.645751311}

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