80=(2*w-5)w

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Solution for 80=(2*w-5)w equation:


Simplifying
80 = (2w + -5) * w

Reorder the terms:
80 = (-5 + 2w) * w

Reorder the terms for easier multiplication:
80 = w(-5 + 2w)
80 = (-5 * w + 2w * w)
80 = (-5w + 2w2)

Solving
80 = -5w + 2w2

Solving for variable 'w'.

Reorder the terms:
80 + 5w + -2w2 = -5w + 5w + 2w2 + -2w2

Combine like terms: -5w + 5w = 0
80 + 5w + -2w2 = 0 + 2w2 + -2w2
80 + 5w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
80 + 5w + -2w2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-40 + -2.5w + w2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -2.5w + 40 + w2 = 0 + 40

Reorder the terms:
-40 + 40 + -2.5w + w2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -2.5w + w2 = 0 + 40
-2.5w + w2 = 0 + 40

Combine like terms: 0 + 40 = 40
-2.5w + w2 = 40

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 = 40 + 1.5625

Reorder the terms:
1.5625 + -2.5w + w2 = 40 + 1.5625

Combine like terms: 40 + 1.5625 = 41.5625
1.5625 + -2.5w + w2 = 41.5625

Factor a perfect square on the left side:
(w + -1.25)(w + -1.25) = 41.5625

Calculate the square root of the right side: 6.446898479

Break this problem into two subproblems by setting 
(w + -1.25) equal to 6.446898479 and -6.446898479.

Subproblem 1

w + -1.25 = 6.446898479 Simplifying w + -1.25 = 6.446898479 Reorder the terms: -1.25 + w = 6.446898479 Solving -1.25 + w = 6.446898479 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 = 6.446898479 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = 6.446898479 + 1.25 w = 6.446898479 + 1.25 Combine like terms: 6.446898479 + 1.25 = 7.696898479 w = 7.696898479 Simplifying w = 7.696898479

Subproblem 2

w + -1.25 = -6.446898479 Simplifying w + -1.25 = -6.446898479 Reorder the terms: -1.25 + w = -6.446898479 Solving -1.25 + w = -6.446898479 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 = -6.446898479 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = -6.446898479 + 1.25 w = -6.446898479 + 1.25 Combine like terms: -6.446898479 + 1.25 = -5.196898479 w = -5.196898479 Simplifying w = -5.196898479

Solution

The solution to the problem is based on the solutions from the subproblems. w = {7.696898479, -5.196898479}

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