w^2-w-18=0

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


Simplifying
w2 + -1w + -18 = 0

Reorder the terms:
-18 + -1w + w2 = 0

Solving
-18 + -1w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -1w + 18 + w2 = 0 + 18

Reorder the terms:
-18 + 18 + -1w + w2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1w + w2 = 0 + 18
-1w + w2 = 0 + 18

Combine like terms: 0 + 18 = 18
-1w + w2 = 18

The w term is -1w.  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.
-1w + 0.25 + w2 = 18 + 0.25

Reorder the terms:
0.25 + -1w + w2 = 18 + 0.25

Combine like terms: 18 + 0.25 = 18.25
0.25 + -1w + w2 = 18.25

Factor a perfect square on the left side:
(w + -0.5)(w + -0.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(w + -0.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

w + -0.5 = 4.272001873 Simplifying w + -0.5 = 4.272001873 Reorder the terms: -0.5 + w = 4.272001873 Solving -0.5 + w = 4.272001873 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 = 4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = 4.272001873 + 0.5 w = 4.272001873 + 0.5 Combine like terms: 4.272001873 + 0.5 = 4.772001873 w = 4.772001873 Simplifying w = 4.772001873

Subproblem 2

w + -0.5 = -4.272001873 Simplifying w + -0.5 = -4.272001873 Reorder the terms: -0.5 + w = -4.272001873 Solving -0.5 + w = -4.272001873 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 = -4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + w = -4.272001873 + 0.5 w = -4.272001873 + 0.5 Combine like terms: -4.272001873 + 0.5 = -3.772001873 w = -3.772001873 Simplifying w = -3.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.772001873, -3.772001873}

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