2w^2-18w-2891=0

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Solution for 2w^2-18w-2891=0 equation:


Simplifying
2w2 + -18w + -2891 = 0

Reorder the terms:
-2891 + -18w + 2w2 = 0

Solving
-2891 + -18w + 2w2 = 0

Solving for variable 'w'.

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

Divide each side by '2'.
-1445.5 + -9w + w2 = 0

Move the constant term to the right:

Add '1445.5' to each side of the equation.
-1445.5 + -9w + 1445.5 + w2 = 0 + 1445.5

Reorder the terms:
-1445.5 + 1445.5 + -9w + w2 = 0 + 1445.5

Combine like terms: -1445.5 + 1445.5 = 0.0
0.0 + -9w + w2 = 0 + 1445.5
-9w + w2 = 0 + 1445.5

Combine like terms: 0 + 1445.5 = 1445.5
-9w + w2 = 1445.5

The w term is -9w.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9w + 20.25 + w2 = 1445.5 + 20.25

Reorder the terms:
20.25 + -9w + w2 = 1445.5 + 20.25

Combine like terms: 1445.5 + 20.25 = 1465.75
20.25 + -9w + w2 = 1465.75

Factor a perfect square on the left side:
(w + -4.5)(w + -4.5) = 1465.75

Calculate the square root of the right side: 38.285114601

Break this problem into two subproblems by setting 
(w + -4.5) equal to 38.285114601 and -38.285114601.

Subproblem 1

w + -4.5 = 38.285114601 Simplifying w + -4.5 = 38.285114601 Reorder the terms: -4.5 + w = 38.285114601 Solving -4.5 + w = 38.285114601 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + w = 38.285114601 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = 38.285114601 + 4.5 w = 38.285114601 + 4.5 Combine like terms: 38.285114601 + 4.5 = 42.785114601 w = 42.785114601 Simplifying w = 42.785114601

Subproblem 2

w + -4.5 = -38.285114601 Simplifying w + -4.5 = -38.285114601 Reorder the terms: -4.5 + w = -38.285114601 Solving -4.5 + w = -38.285114601 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + w = -38.285114601 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + w = -38.285114601 + 4.5 w = -38.285114601 + 4.5 Combine like terms: -38.285114601 + 4.5 = -33.785114601 w = -33.785114601 Simplifying w = -33.785114601

Solution

The solution to the problem is based on the solutions from the subproblems. w = {42.785114601, -33.785114601}

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