w^2-5w+7-35=0

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Solution for w^2-5w+7-35=0 equation: 


Simplifying
w2 + -5w + 7 + -35 = 0

Reorder the terms:
7 + -35 + -5w + w2 = 0

Combine like terms: 7 + -35 = -28
-28 + -5w + w2 = 0

Solving
-28 + -5w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -5w + 28 + w2 = 0 + 28

Reorder the terms:
-28 + 28 + -5w + w2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -5w + w2 = 0 + 28
-5w + w2 = 0 + 28

Combine like terms: 0 + 28 = 28
-5w + w2 = 28

The w term is -5w.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5w + 6.25 + w2 = 28 + 6.25

Reorder the terms:
6.25 + -5w + w2 = 28 + 6.25

Combine like terms: 28 + 6.25 = 34.25
6.25 + -5w + w2 = 34.25

Factor a perfect square on the left side:
(w + -2.5)(w + -2.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(w + -2.5) equal to 5.852349955 and -5.852349955.


Subproblem 1
w + -2.5 = 5.852349955

Simplifying
w + -2.5 = 5.852349955

Reorder the terms:
-2.5 + w = 5.852349955

Solving
-2.5 + w = 5.852349955

Solving for variable 'w'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + w = 5.852349955 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + w = 5.852349955 + 2.5
w = 5.852349955 + 2.5

Combine like terms: 5.852349955 + 2.5 = 8.352349955
w = 8.352349955

Simplifying
w = 8.352349955


Subproblem 2
w + -2.5 = -5.852349955

Simplifying
w + -2.5 = -5.852349955

Reorder the terms:
-2.5 + w = -5.852349955

Solving
-2.5 + w = -5.852349955

Solving for variable 'w'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + w = -5.852349955 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + w = -5.852349955 + 2.5
w = -5.852349955 + 2.5

Combine like terms: -5.852349955 + 2.5 = -3.352349955
w = -3.352349955

Simplifying
w = -3.352349955


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.352349955, -3.352349955}

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