w^2-25w+75=0

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Solution for w^2-25w+75=0 equation: 


Simplifying
w2 + -25w + 75 = 0

Reorder the terms:
75 + -25w + w2 = 0

Solving
75 + -25w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '-75' to each side of the equation.
75 + -25w + -75 + w2 = 0 + -75

Reorder the terms:
75 + -75 + -25w + w2 = 0 + -75

Combine like terms: 75 + -75 = 0
0 + -25w + w2 = 0 + -75
-25w + w2 = 0 + -75

Combine like terms: 0 + -75 = -75
-25w + w2 = -75

The w term is -25w.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25w + 156.25 + w2 = -75 + 156.25

Reorder the terms:
156.25 + -25w + w2 = -75 + 156.25

Combine like terms: -75 + 156.25 = 81.25
156.25 + -25w + w2 = 81.25

Factor a perfect square on the left side:
(w + -12.5)(w + -12.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(w + -12.5) equal to 9.013878189 and -9.013878189.


Subproblem 1
w + -12.5 = 9.013878189

Simplifying
w + -12.5 = 9.013878189

Reorder the terms:
-12.5 + w = 9.013878189

Solving
-12.5 + w = 9.013878189

Solving for variable 'w'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + w = 9.013878189 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + w = 9.013878189 + 12.5
w = 9.013878189 + 12.5

Combine like terms: 9.013878189 + 12.5 = 21.513878189
w = 21.513878189

Simplifying
w = 21.513878189


Subproblem 2
w + -12.5 = -9.013878189

Simplifying
w + -12.5 = -9.013878189

Reorder the terms:
-12.5 + w = -9.013878189

Solving
-12.5 + w = -9.013878189

Solving for variable 'w'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + w = -9.013878189 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + w = -9.013878189 + 12.5
w = -9.013878189 + 12.5

Combine like terms: -9.013878189 + 12.5 = 3.486121811
w = 3.486121811

Simplifying
w = 3.486121811


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {21.513878189, 3.486121811}

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