w^2-100w-1875=0

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Solution for w^2-100w-1875=0 equation:


Simplifying
w2 + -100w + -1875 = 0

Reorder the terms:
-1875 + -100w + w2 = 0

Solving
-1875 + -100w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '1875' to each side of the equation.
-1875 + -100w + 1875 + w2 = 0 + 1875

Reorder the terms:
-1875 + 1875 + -100w + w2 = 0 + 1875

Combine like terms: -1875 + 1875 = 0
0 + -100w + w2 = 0 + 1875
-100w + w2 = 0 + 1875

Combine like terms: 0 + 1875 = 1875
-100w + w2 = 1875

The w term is -100w.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100w + 2500 + w2 = 1875 + 2500

Reorder the terms:
2500 + -100w + w2 = 1875 + 2500

Combine like terms: 1875 + 2500 = 4375
2500 + -100w + w2 = 4375

Factor a perfect square on the left side:
(w + -50)(w + -50) = 4375

Calculate the square root of the right side: 66.143782777

Break this problem into two subproblems by setting 
(w + -50) equal to 66.143782777 and -66.143782777.

Subproblem 1

w + -50 = 66.143782777 Simplifying w + -50 = 66.143782777 Reorder the terms: -50 + w = 66.143782777 Solving -50 + w = 66.143782777 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + w = 66.143782777 + 50 Combine like terms: -50 + 50 = 0 0 + w = 66.143782777 + 50 w = 66.143782777 + 50 Combine like terms: 66.143782777 + 50 = 116.143782777 w = 116.143782777 Simplifying w = 116.143782777

Subproblem 2

w + -50 = -66.143782777 Simplifying w + -50 = -66.143782777 Reorder the terms: -50 + w = -66.143782777 Solving -50 + w = -66.143782777 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + w = -66.143782777 + 50 Combine like terms: -50 + 50 = 0 0 + w = -66.143782777 + 50 w = -66.143782777 + 50 Combine like terms: -66.143782777 + 50 = -16.143782777 w = -16.143782777 Simplifying w = -16.143782777

Solution

The solution to the problem is based on the solutions from the subproblems. w = {116.143782777, -16.143782777}

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