500=w(w+20)

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Solution for 500=w(w+20) equation:


Simplifying
500 = w(w + 20)

Reorder the terms:
500 = w(20 + w)
500 = (20 * w + w * w)
500 = (20w + w2)

Solving
500 = 20w + w2

Solving for variable 'w'.

Reorder the terms:
500 + -20w + -1w2 = 20w + -20w + w2 + -1w2

Combine like terms: 20w + -20w = 0
500 + -20w + -1w2 = 0 + w2 + -1w2
500 + -20w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
500 + -20w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-500 + 20w + w2 = 0

Move the constant term to the right:

Add '500' to each side of the equation.
-500 + 20w + 500 + w2 = 0 + 500

Reorder the terms:
-500 + 500 + 20w + w2 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 20w + w2 = 0 + 500
20w + w2 = 0 + 500

Combine like terms: 0 + 500 = 500
20w + w2 = 500

The w term is 20w.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20w + 100 + w2 = 500 + 100

Reorder the terms:
100 + 20w + w2 = 500 + 100

Combine like terms: 500 + 100 = 600
100 + 20w + w2 = 600

Factor a perfect square on the left side:
(w + 10)(w + 10) = 600

Calculate the square root of the right side: 24.494897428

Break this problem into two subproblems by setting 
(w + 10) equal to 24.494897428 and -24.494897428.

Subproblem 1

w + 10 = 24.494897428 Simplifying w + 10 = 24.494897428 Reorder the terms: 10 + w = 24.494897428 Solving 10 + w = 24.494897428 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = 24.494897428 + -10 Combine like terms: 10 + -10 = 0 0 + w = 24.494897428 + -10 w = 24.494897428 + -10 Combine like terms: 24.494897428 + -10 = 14.494897428 w = 14.494897428 Simplifying w = 14.494897428

Subproblem 2

w + 10 = -24.494897428 Simplifying w + 10 = -24.494897428 Reorder the terms: 10 + w = -24.494897428 Solving 10 + w = -24.494897428 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = -24.494897428 + -10 Combine like terms: 10 + -10 = 0 0 + w = -24.494897428 + -10 w = -24.494897428 + -10 Combine like terms: -24.494897428 + -10 = -34.494897428 w = -34.494897428 Simplifying w = -34.494897428

Solution

The solution to the problem is based on the solutions from the subproblems. w = {14.494897428, -34.494897428}

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