(w-7)(w-7)+2=34

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Solution for (w-7)(w-7)+2=34 equation: 


Simplifying
(w + -7)(w + -7) + 2 = 34

Reorder the terms:
(-7 + w)(w + -7) + 2 = 34

Reorder the terms:
(-7 + w)(-7 + w) + 2 = 34

Multiply (-7 + w) * (-7 + w)
(-7(-7 + w) + w(-7 + w)) + 2 = 34
((-7 * -7 + w * -7) + w(-7 + w)) + 2 = 34
((49 + -7w) + w(-7 + w)) + 2 = 34
(49 + -7w + (-7 * w + w * w)) + 2 = 34
(49 + -7w + (-7w + w2)) + 2 = 34

Combine like terms: -7w + -7w = -14w
(49 + -14w + w2) + 2 = 34

Reorder the terms:
49 + 2 + -14w + w2 = 34

Combine like terms: 49 + 2 = 51
51 + -14w + w2 = 34

Solving
51 + -14w + w2 = 34

Solving for variable 'w'.

Reorder the terms:
51 + -34 + -14w + w2 = 34 + -34

Combine like terms: 51 + -34 = 17
17 + -14w + w2 = 34 + -34

Combine like terms: 34 + -34 = 0
17 + -14w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -14w + -17 + w2 = 0 + -17

Reorder the terms:
17 + -17 + -14w + w2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -14w + w2 = 0 + -17
-14w + w2 = 0 + -17

Combine like terms: 0 + -17 = -17
-14w + w2 = -17

The w term is -14w.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14w + 49 + w2 = -17 + 49

Reorder the terms:
49 + -14w + w2 = -17 + 49

Combine like terms: -17 + 49 = 32
49 + -14w + w2 = 32

Factor a perfect square on the left side:
(w + -7)(w + -7) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(w + -7) equal to 5.656854249 and -5.656854249.


Subproblem 1
w + -7 = 5.656854249

Simplifying
w + -7 = 5.656854249

Reorder the terms:
-7 + w = 5.656854249

Solving
-7 + w = 5.656854249

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + w = 5.656854249 + 7

Combine like terms: -7 + 7 = 0
0 + w = 5.656854249 + 7
w = 5.656854249 + 7

Combine like terms: 5.656854249 + 7 = 12.656854249
w = 12.656854249

Simplifying
w = 12.656854249


Subproblem 2
w + -7 = -5.656854249

Simplifying
w + -7 = -5.656854249

Reorder the terms:
-7 + w = -5.656854249

Solving
-7 + w = -5.656854249

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + w = -5.656854249 + 7

Combine like terms: -7 + 7 = 0
0 + w = -5.656854249 + 7
w = -5.656854249 + 7

Combine like terms: -5.656854249 + 7 = 1.343145751
w = 1.343145751

Simplifying
w = 1.343145751


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {12.656854249, 1.343145751}

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