(w^2)-8w-12=0

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Solution for (w^2)-8w-12=0 equation:


Simplifying
(w2) + -8w + -12 = 0
w2 + -8w + -12 = 0

Reorder the terms:
-12 + -8w + w2 = 0

Solving
-12 + -8w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -8w + 12 + w2 = 0 + 12

Reorder the terms:
-12 + 12 + -8w + w2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -8w + w2 = 0 + 12
-8w + w2 = 0 + 12

Combine like terms: 0 + 12 = 12
-8w + w2 = 12

The w term is -8w.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8w + 16 + w2 = 12 + 16

Reorder the terms:
16 + -8w + w2 = 12 + 16

Combine like terms: 12 + 16 = 28
16 + -8w + w2 = 28

Factor a perfect square on the left side:
(w + -4)(w + -4) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(w + -4) equal to 5.291502622 and -5.291502622.

Subproblem 1

w + -4 = 5.291502622 Simplifying w + -4 = 5.291502622 Reorder the terms: -4 + w = 5.291502622 Solving -4 + w = 5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 5.291502622 + 4 Combine like terms: -4 + 4 = 0 0 + w = 5.291502622 + 4 w = 5.291502622 + 4 Combine like terms: 5.291502622 + 4 = 9.291502622 w = 9.291502622 Simplifying w = 9.291502622

Subproblem 2

w + -4 = -5.291502622 Simplifying w + -4 = -5.291502622 Reorder the terms: -4 + w = -5.291502622 Solving -4 + w = -5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = -5.291502622 + 4 Combine like terms: -4 + 4 = 0 0 + w = -5.291502622 + 4 w = -5.291502622 + 4 Combine like terms: -5.291502622 + 4 = -1.291502622 w = -1.291502622 Simplifying w = -1.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. w = {9.291502622, -1.291502622}

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