w^2+2w-27=0

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Solution for w^2+2w-27=0 equation:


Simplifying
w2 + 2w + -27 = 0

Reorder the terms:
-27 + 2w + w2 = 0

Solving
-27 + 2w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + 2w + 27 + w2 = 0 + 27

Reorder the terms:
-27 + 27 + 2w + w2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + 2w + w2 = 0 + 27
2w + w2 = 0 + 27

Combine like terms: 0 + 27 = 27
2w + w2 = 27

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 27 + 1

Reorder the terms:
1 + 2w + w2 = 27 + 1

Combine like terms: 27 + 1 = 28
1 + 2w + w2 = 28

Factor a perfect square on the left side:
(w + 1)(w + 1) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(w + 1) equal to 5.291502622 and -5.291502622.

Subproblem 1

w + 1 = 5.291502622 Simplifying w + 1 = 5.291502622 Reorder the terms: 1 + w = 5.291502622 Solving 1 + w = 5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 5.291502622 + -1 Combine like terms: 1 + -1 = 0 0 + w = 5.291502622 + -1 w = 5.291502622 + -1 Combine like terms: 5.291502622 + -1 = 4.291502622 w = 4.291502622 Simplifying w = 4.291502622

Subproblem 2

w + 1 = -5.291502622 Simplifying w + 1 = -5.291502622 Reorder the terms: 1 + w = -5.291502622 Solving 1 + w = -5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -5.291502622 + -1 Combine like terms: 1 + -1 = 0 0 + w = -5.291502622 + -1 w = -5.291502622 + -1 Combine like terms: -5.291502622 + -1 = -6.291502622 w = -6.291502622 Simplifying w = -6.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.291502622, -6.291502622}

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