8=5w(w+4)

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Solution for 8=5w(w+4) equation:


Simplifying
8 = 5w(w + 4)

Reorder the terms:
8 = 5w(4 + w)
8 = (4 * 5w + w * 5w)
8 = (20w + 5w2)

Solving
8 = 20w + 5w2

Solving for variable 'w'.

Reorder the terms:
8 + -20w + -5w2 = 20w + -20w + 5w2 + -5w2

Combine like terms: 20w + -20w = 0
8 + -20w + -5w2 = 0 + 5w2 + -5w2
8 + -20w + -5w2 = 5w2 + -5w2

Combine like terms: 5w2 + -5w2 = 0
8 + -20w + -5w2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.6 + 4w + w2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 4w + 1.6 + w2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 4w + w2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 4w + w2 = 0 + 1.6
4w + w2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
4w + w2 = 1.6

The w term is 4w.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4w + 4 + w2 = 1.6 + 4

Reorder the terms:
4 + 4w + w2 = 1.6 + 4

Combine like terms: 1.6 + 4 = 5.6
4 + 4w + w2 = 5.6

Factor a perfect square on the left side:
(w + 2)(w + 2) = 5.6

Calculate the square root of the right side: 2.366431913

Break this problem into two subproblems by setting 
(w + 2) equal to 2.366431913 and -2.366431913.

Subproblem 1

w + 2 = 2.366431913 Simplifying w + 2 = 2.366431913 Reorder the terms: 2 + w = 2.366431913 Solving 2 + w = 2.366431913 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 2.366431913 + -2 Combine like terms: 2 + -2 = 0 0 + w = 2.366431913 + -2 w = 2.366431913 + -2 Combine like terms: 2.366431913 + -2 = 0.366431913 w = 0.366431913 Simplifying w = 0.366431913

Subproblem 2

w + 2 = -2.366431913 Simplifying w + 2 = -2.366431913 Reorder the terms: 2 + w = -2.366431913 Solving 2 + w = -2.366431913 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = -2.366431913 + -2 Combine like terms: 2 + -2 = 0 0 + w = -2.366431913 + -2 w = -2.366431913 + -2 Combine like terms: -2.366431913 + -2 = -4.366431913 w = -4.366431913 Simplifying w = -4.366431913

Solution

The solution to the problem is based on the solutions from the subproblems. w = {0.366431913, -4.366431913}

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