w^2-12w+8=0

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


Simplifying
w2 + -12w + 8 = 0

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

Solving
8 + -12w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The w term is -12w.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12w + 36 + w2 = -8 + 36

Reorder the terms:
36 + -12w + w2 = -8 + 36

Combine like terms: -8 + 36 = 28
36 + -12w + w2 = 28

Factor a perfect square on the left side:
(w + -6)(w + -6) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(w + -6) equal to 5.291502622 and -5.291502622.

Subproblem 1

w + -6 = 5.291502622 Simplifying w + -6 = 5.291502622 Reorder the terms: -6 + w = 5.291502622 Solving -6 + w = 5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + w = 5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + w = 5.291502622 + 6 w = 5.291502622 + 6 Combine like terms: 5.291502622 + 6 = 11.291502622 w = 11.291502622 Simplifying w = 11.291502622

Subproblem 2

w + -6 = -5.291502622 Simplifying w + -6 = -5.291502622 Reorder the terms: -6 + w = -5.291502622 Solving -6 + w = -5.291502622 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + w = -5.291502622 + 6 Combine like terms: -6 + 6 = 0 0 + w = -5.291502622 + 6 w = -5.291502622 + 6 Combine like terms: -5.291502622 + 6 = 0.708497378 w = 0.708497378 Simplifying w = 0.708497378

Solution

The solution to the problem is based on the solutions from the subproblems. w = {11.291502622, 0.708497378}

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