50w=20(w^2-6.25)

Solution for 50w=20(w^2-6.25) equation:

Simplifying
50w = 20(w2 + -6.25)

Reorder the terms:
50w = 20(-6.25 + w2)
50w = (-6.25 * 20 + w2 * 20)
50w = (-125 + 20w2)

Solving
50w = -125 + 20w2

Solving for variable 'w'.

Reorder the terms:
125 + 50w + -20w2 = -125 + 20w2 + 125 + -20w2

Reorder the terms:
125 + 50w + -20w2 = -125 + 125 + 20w2 + -20w2

Combine like terms: -125 + 125 = 0
125 + 50w + -20w2 = 0 + 20w2 + -20w2
125 + 50w + -20w2 = 20w2 + -20w2

Combine like terms: 20w2 + -20w2 = 0
125 + 50w + -20w2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(25 + 10w + -4w2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(25 + 10w + -4w2)' equal to zero and attempt to solve:

Simplifying
25 + 10w + -4w2 = 0

Solving
25 + 10w + -4w2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-6.25 + -2.5w + w2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -2.5w + 6.25 + w2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -2.5w + w2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -2.5w + w2 = 0 + 6.25
-2.5w + w2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-2.5w + w2 = 6.25

The w term is -2.5w.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5w + 1.5625 + w2 = 6.25 + 1.5625

Reorder the terms:
1.5625 + -2.5w + w2 = 6.25 + 1.5625

Combine like terms: 6.25 + 1.5625 = 7.8125
1.5625 + -2.5w + w2 = 7.8125

Factor a perfect square on the left side:
(w + -1.25)(w + -1.25) = 7.8125

Calculate the square root of the right side: 2.795084972

Break this problem into two subproblems by setting 
(w + -1.25) equal to 2.795084972 and -2.795084972.

Subproblem 1
w + -1.25 = 2.795084972

Simplifying
w + -1.25 = 2.795084972

Reorder the terms:
-1.25 + w = 2.795084972

Solving
-1.25 + w = 2.795084972

Solving for variable 'w'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + w = 2.795084972 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + w = 2.795084972 + 1.25
w = 2.795084972 + 1.25

Combine like terms: 2.795084972 + 1.25 = 4.045084972
w = 4.045084972

Simplifying
w = 4.045084972

Subproblem 2
w + -1.25 = -2.795084972

Simplifying
w + -1.25 = -2.795084972

Reorder the terms:
-1.25 + w = -2.795084972

Solving
-1.25 + w = -2.795084972

Solving for variable 'w'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + w = -2.795084972 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + w = -2.795084972 + 1.25
w = -2.795084972 + 1.25

Combine like terms: -2.795084972 + 1.25 = -1.545084972
w = -1.545084972

Simplifying
w = -1.545084972

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.045084972, -1.545084972}
Solution
w = {4.045084972, -1.545084972}