35=w*(2w-5)

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Solution for 35=w*(2w-5) equation:


Simplifying
35 = w(2w + -5)

Reorder the terms:
35 = w(-5 + 2w)
35 = (-5 * w + 2w * w)
35 = (-5w + 2w2)

Solving
35 = -5w + 2w2

Solving for variable 'w'.

Reorder the terms:
35 + 5w + -2w2 = -5w + 5w + 2w2 + -2w2

Combine like terms: -5w + 5w = 0
35 + 5w + -2w2 = 0 + 2w2 + -2w2
35 + 5w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
35 + 5w + -2w2 = 0

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

Divide each side by '-2'.
-17.5 + -2.5w + w2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + -2.5w + 17.5 + w2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + -2.5w + w2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + -2.5w + w2 = 0 + 17.5
-2.5w + w2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
-2.5w + w2 = 17.5

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 = 17.5 + 1.5625

Reorder the terms:
1.5625 + -2.5w + w2 = 17.5 + 1.5625

Combine like terms: 17.5 + 1.5625 = 19.0625
1.5625 + -2.5w + w2 = 19.0625

Factor a perfect square on the left side:
(w + -1.25)(w + -1.25) = 19.0625

Calculate the square root of the right side: 4.366062299

Break this problem into two subproblems by setting 
(w + -1.25) equal to 4.366062299 and -4.366062299.

Subproblem 1

w + -1.25 = 4.366062299 Simplifying w + -1.25 = 4.366062299 Reorder the terms: -1.25 + w = 4.366062299 Solving -1.25 + w = 4.366062299 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 = 4.366062299 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = 4.366062299 + 1.25 w = 4.366062299 + 1.25 Combine like terms: 4.366062299 + 1.25 = 5.616062299 w = 5.616062299 Simplifying w = 5.616062299

Subproblem 2

w + -1.25 = -4.366062299 Simplifying w + -1.25 = -4.366062299 Reorder the terms: -1.25 + w = -4.366062299 Solving -1.25 + w = -4.366062299 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 = -4.366062299 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + w = -4.366062299 + 1.25 w = -4.366062299 + 1.25 Combine like terms: -4.366062299 + 1.25 = -3.116062299 w = -3.116062299 Simplifying w = -3.116062299

Solution

The solution to the problem is based on the solutions from the subproblems. w = {5.616062299, -3.116062299}

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