-w^2+75w-1200=0

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Solution for -w^2+75w-1200=0 equation:


Simplifying
-1w2 + 75w + -1200 = 0

Reorder the terms:
-1200 + 75w + -1w2 = 0

Solving
-1200 + 75w + -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'.
1200 + -75w + w2 = 0

Move the constant term to the right:

Add '-1200' to each side of the equation.
1200 + -75w + -1200 + w2 = 0 + -1200

Reorder the terms:
1200 + -1200 + -75w + w2 = 0 + -1200

Combine like terms: 1200 + -1200 = 0
0 + -75w + w2 = 0 + -1200
-75w + w2 = 0 + -1200

Combine like terms: 0 + -1200 = -1200
-75w + w2 = -1200

The w term is -75w.  Take half its coefficient (-37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
-75w + 1406.25 + w2 = -1200 + 1406.25

Reorder the terms:
1406.25 + -75w + w2 = -1200 + 1406.25

Combine like terms: -1200 + 1406.25 = 206.25
1406.25 + -75w + w2 = 206.25

Factor a perfect square on the left side:
(w + -37.5)(w + -37.5) = 206.25

Calculate the square root of the right side: 14.361406616

Break this problem into two subproblems by setting 
(w + -37.5) equal to 14.361406616 and -14.361406616.

Subproblem 1

w + -37.5 = 14.361406616 Simplifying w + -37.5 = 14.361406616 Reorder the terms: -37.5 + w = 14.361406616 Solving -37.5 + w = 14.361406616 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + w = 14.361406616 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + w = 14.361406616 + 37.5 w = 14.361406616 + 37.5 Combine like terms: 14.361406616 + 37.5 = 51.861406616 w = 51.861406616 Simplifying w = 51.861406616

Subproblem 2

w + -37.5 = -14.361406616 Simplifying w + -37.5 = -14.361406616 Reorder the terms: -37.5 + w = -14.361406616 Solving -37.5 + w = -14.361406616 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + w = -14.361406616 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + w = -14.361406616 + 37.5 w = -14.361406616 + 37.5 Combine like terms: -14.361406616 + 37.5 = 23.138593384 w = 23.138593384 Simplifying w = 23.138593384

Solution

The solution to the problem is based on the solutions from the subproblems. w = {51.861406616, 23.138593384}

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