-w^2+87w-600=0

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Solution for -w^2+87w-600=0 equation:


Simplifying
-1w2 + 87w + -600 = 0

Reorder the terms:
-600 + 87w + -1w2 = 0

Solving
-600 + 87w + -1w2 = 0

Solving for variable 'w'.

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

Divide each side by '-1'.
600 + -87w + w2 = 0

Move the constant term to the right:

Add '-600' to each side of the equation.
600 + -87w + -600 + w2 = 0 + -600

Reorder the terms:
600 + -600 + -87w + w2 = 0 + -600

Combine like terms: 600 + -600 = 0
0 + -87w + w2 = 0 + -600
-87w + w2 = 0 + -600

Combine like terms: 0 + -600 = -600
-87w + w2 = -600

The w term is -87w.  Take half its coefficient (-43.5).
Square it (1892.25) and add it to both sides.

Add '1892.25' to each side of the equation.
-87w + 1892.25 + w2 = -600 + 1892.25

Reorder the terms:
1892.25 + -87w + w2 = -600 + 1892.25

Combine like terms: -600 + 1892.25 = 1292.25
1892.25 + -87w + w2 = 1292.25

Factor a perfect square on the left side:
(w + -43.5)(w + -43.5) = 1292.25

Calculate the square root of the right side: 35.947878936

Break this problem into two subproblems by setting 
(w + -43.5) equal to 35.947878936 and -35.947878936.

Subproblem 1

w + -43.5 = 35.947878936 Simplifying w + -43.5 = 35.947878936 Reorder the terms: -43.5 + w = 35.947878936 Solving -43.5 + w = 35.947878936 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '43.5' to each side of the equation. -43.5 + 43.5 + w = 35.947878936 + 43.5 Combine like terms: -43.5 + 43.5 = 0.0 0.0 + w = 35.947878936 + 43.5 w = 35.947878936 + 43.5 Combine like terms: 35.947878936 + 43.5 = 79.447878936 w = 79.447878936 Simplifying w = 79.447878936

Subproblem 2

w + -43.5 = -35.947878936 Simplifying w + -43.5 = -35.947878936 Reorder the terms: -43.5 + w = -35.947878936 Solving -43.5 + w = -35.947878936 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '43.5' to each side of the equation. -43.5 + 43.5 + w = -35.947878936 + 43.5 Combine like terms: -43.5 + 43.5 = 0.0 0.0 + w = -35.947878936 + 43.5 w = -35.947878936 + 43.5 Combine like terms: -35.947878936 + 43.5 = 7.552121064 w = 7.552121064 Simplifying w = 7.552121064

Solution

The solution to the problem is based on the solutions from the subproblems. w = {79.447878936, 7.552121064}

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