-w^2-5w=84+0

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Solution for -w^2-5w=84+0 equation: 


Simplifying
-1w2 + -5w = 84 + 0

Reorder the terms:
-5w + -1w2 = 84 + 0

Combine like terms: 84 + 0 = 84
-5w + -1w2 = 84

Solving
-5w + -1w2 = 84

Solving for variable 'w'.

Reorder the terms:
-84 + -5w + -1w2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + -5w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(84 + 5w + w2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(84 + 5w + w2)' equal to zero and attempt to solve:

Simplifying
84 + 5w + w2 = 0

Solving
84 + 5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-84' to each side of the equation.
84 + 5w + -84 + w2 = 0 + -84

Reorder the terms:
84 + -84 + 5w + w2 = 0 + -84

Combine like terms: 84 + -84 = 0
0 + 5w + w2 = 0 + -84
5w + w2 = 0 + -84

Combine like terms: 0 + -84 = -84
5w + w2 = -84

The w term is 5w.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5w + 6.25 + w2 = -84 + 6.25

Reorder the terms:
6.25 + 5w + w2 = -84 + 6.25

Combine like terms: -84 + 6.25 = -77.75
6.25 + 5w + w2 = -77.75

Factor a perfect square on the left side:
(w + 2.5)(w + 2.5) = -77.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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