w^2+7-6w=0

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Solution for w^2+7-6w=0 equation: 


Simplifying
w2 + 7 + -6w = 0

Reorder the terms:
7 + -6w + w2 = 0

Solving
7 + -6w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -6w + -7 + w2 = 0 + -7

Reorder the terms:
7 + -7 + -6w + w2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6w + w2 = 0 + -7
-6w + w2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6w + w2 = -7

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 = -7 + 9

Reorder the terms:
9 + -6w + w2 = -7 + 9

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

Factor a perfect square on the left side:
(w + -3)(w + -3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(w + -3) equal to 1.414213562 and -1.414213562.


Subproblem 1
w + -3 = 1.414213562

Simplifying
w + -3 = 1.414213562

Reorder the terms:
-3 + w = 1.414213562

Solving
-3 + w = 1.414213562

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 = 1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + w = 1.414213562 + 3
w = 1.414213562 + 3

Combine like terms: 1.414213562 + 3 = 4.414213562
w = 4.414213562

Simplifying
w = 4.414213562


Subproblem 2
w + -3 = -1.414213562

Simplifying
w + -3 = -1.414213562

Reorder the terms:
-3 + w = -1.414213562

Solving
-3 + w = -1.414213562

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 = -1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + w = -1.414213562 + 3
w = -1.414213562 + 3

Combine like terms: -1.414213562 + 3 = 1.585786438
w = 1.585786438

Simplifying
w = 1.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.414213562, 1.585786438}

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