w^2+w-1000=0

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Solution for w^2+w-1000=0 equation:


Simplifying
w2 + w + -1000 = 0

Reorder the terms:
-1000 + w + w2 = 0

Solving
-1000 + w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '1000' to each side of the equation.
-1000 + w + 1000 + w2 = 0 + 1000

Reorder the terms:
-1000 + 1000 + w + w2 = 0 + 1000

Combine like terms: -1000 + 1000 = 0
0 + w + w2 = 0 + 1000
w + w2 = 0 + 1000

Combine like terms: 0 + 1000 = 1000
w + w2 = 1000

The w term is w.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
w + 0.25 + w2 = 1000 + 0.25

Reorder the terms:
0.25 + w + w2 = 1000 + 0.25

Combine like terms: 1000 + 0.25 = 1000.25
0.25 + w + w2 = 1000.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 1000.25

Calculate the square root of the right side: 31.626729202

Break this problem into two subproblems by setting 
(w + 0.5) equal to 31.626729202 and -31.626729202.

Subproblem 1

w + 0.5 = 31.626729202 Simplifying w + 0.5 = 31.626729202 Reorder the terms: 0.5 + w = 31.626729202 Solving 0.5 + w = 31.626729202 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = 31.626729202 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 31.626729202 + -0.5 w = 31.626729202 + -0.5 Combine like terms: 31.626729202 + -0.5 = 31.126729202 w = 31.126729202 Simplifying w = 31.126729202

Subproblem 2

w + 0.5 = -31.626729202 Simplifying w + 0.5 = -31.626729202 Reorder the terms: 0.5 + w = -31.626729202 Solving 0.5 + w = -31.626729202 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + w = -31.626729202 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -31.626729202 + -0.5 w = -31.626729202 + -0.5 Combine like terms: -31.626729202 + -0.5 = -32.126729202 w = -32.126729202 Simplifying w = -32.126729202

Solution

The solution to the problem is based on the solutions from the subproblems. w = {31.126729202, -32.126729202}

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