w^2+w+-120=0

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Solution for w^2+w+-120=0 equation:


Simplifying
w2 + w + -120 = 0

Reorder the terms:
-120 + w + w2 = 0

Solving
-120 + w + w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + w + 120 + w2 = 0 + 120

Reorder the terms:
-120 + 120 + w + w2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + w + w2 = 0 + 120
w + w2 = 0 + 120

Combine like terms: 0 + 120 = 120
w + w2 = 120

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 = 120 + 0.25

Reorder the terms:
0.25 + w + w2 = 120 + 0.25

Combine like terms: 120 + 0.25 = 120.25
0.25 + w + w2 = 120.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(w + 0.5) equal to 10.9658561 and -10.9658561.

Subproblem 1

w + 0.5 = 10.9658561 Simplifying w + 0.5 = 10.9658561 Reorder the terms: 0.5 + w = 10.9658561 Solving 0.5 + w = 10.9658561 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 = 10.9658561 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = 10.9658561 + -0.5 w = 10.9658561 + -0.5 Combine like terms: 10.9658561 + -0.5 = 10.4658561 w = 10.4658561 Simplifying w = 10.4658561

Subproblem 2

w + 0.5 = -10.9658561 Simplifying w + 0.5 = -10.9658561 Reorder the terms: 0.5 + w = -10.9658561 Solving 0.5 + w = -10.9658561 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 = -10.9658561 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + w = -10.9658561 + -0.5 w = -10.9658561 + -0.5 Combine like terms: -10.9658561 + -0.5 = -11.4658561 w = -11.4658561 Simplifying w = -11.4658561

Solution

The solution to the problem is based on the solutions from the subproblems. w = {10.4658561, -11.4658561}

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