(w^2)+(w+15)=1000

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Solution for (w^2)+(w+15)=1000 equation:


Simplifying
(w2) + (w + 15) = 1000
w2 + (w + 15) = 1000

Reorder the terms:
w2 + (15 + w) = 1000

Remove parenthesis around (15 + w)
w2 + 15 + w = 1000

Reorder the terms:
15 + w + w2 = 1000

Solving
15 + w + w2 = 1000

Solving for variable 'w'.

Reorder the terms:
15 + -1000 + w + w2 = 1000 + -1000

Combine like terms: 15 + -1000 = -985
-985 + w + w2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-985 + w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '985' to each side of the equation.
-985 + w + 985 + w2 = 0 + 985

Reorder the terms:
-985 + 985 + w + w2 = 0 + 985

Combine like terms: -985 + 985 = 0
0 + w + w2 = 0 + 985
w + w2 = 0 + 985

Combine like terms: 0 + 985 = 985
w + w2 = 985

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 = 985 + 0.25

Reorder the terms:
0.25 + w + w2 = 985 + 0.25

Combine like terms: 985 + 0.25 = 985.25
0.25 + w + w2 = 985.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 985.25

Calculate the square root of the right side: 31.388692231

Break this problem into two subproblems by setting 
(w + 0.5) equal to 31.388692231 and -31.388692231.

Subproblem 1

w + 0.5 = 31.388692231 Simplifying w + 0.5 = 31.388692231 Reorder the terms: 0.5 + w = 31.388692231 Solving 0.5 + w = 31.388692231 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 = 31.388692231 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 31.388692231 + -0.5 w = 31.388692231 + -0.5 Combine like terms: 31.388692231 + -0.5 = 30.888692231 w = 30.888692231 Simplifying w = 30.888692231

Subproblem 2

w + 0.5 = -31.388692231 Simplifying w + 0.5 = -31.388692231 Reorder the terms: 0.5 + w = -31.388692231 Solving 0.5 + w = -31.388692231 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 = -31.388692231 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -31.388692231 + -0.5 w = -31.388692231 + -0.5 Combine like terms: -31.388692231 + -0.5 = -31.888692231 w = -31.888692231 Simplifying w = -31.888692231

Solution

The solution to the problem is based on the solutions from the subproblems. w = {30.888692231, -31.888692231}

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