=5w^2+6w+34

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Solution for =5w^2+6w+34 equation: 


Simplifying
0 = 5w2 + 6w + 34

Reorder the terms:
0 = 34 + 6w + 5w2

Solving
0 = 34 + 6w + 5w2

Solving for variable 'w'.

Combine like terms: 0 + -34 = -34
-34 + -6w + -5w2 = 34 + 6w + 5w2 + -34 + -6w + -5w2

Reorder the terms:
-34 + -6w + -5w2 = 34 + -34 + 6w + -6w + 5w2 + -5w2

Combine like terms: 34 + -34 = 0
-34 + -6w + -5w2 = 0 + 6w + -6w + 5w2 + -5w2
-34 + -6w + -5w2 = 6w + -6w + 5w2 + -5w2

Combine like terms: 6w + -6w = 0
-34 + -6w + -5w2 = 0 + 5w2 + -5w2
-34 + -6w + -5w2 = 5w2 + -5w2

Combine like terms: 5w2 + -5w2 = 0
-34 + -6w + -5w2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(34 + 6w + 5w2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(34 + 6w + 5w2)' equal to zero and attempt to solve:

Simplifying
34 + 6w + 5w2 = 0

Solving
34 + 6w + 5w2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
6.8 + 1.2w + w2 = 0

Move the constant term to the right:

Add '-6.8' to each side of the equation.
6.8 + 1.2w + -6.8 + w2 = 0 + -6.8

Reorder the terms:
6.8 + -6.8 + 1.2w + w2 = 0 + -6.8

Combine like terms: 6.8 + -6.8 = 0.0
0.0 + 1.2w + w2 = 0 + -6.8
1.2w + w2 = 0 + -6.8

Combine like terms: 0 + -6.8 = -6.8
1.2w + w2 = -6.8

The w term is 1.2w.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2w + 0.36 + w2 = -6.8 + 0.36

Reorder the terms:
0.36 + 1.2w + w2 = -6.8 + 0.36

Combine like terms: -6.8 + 0.36 = -6.44
0.36 + 1.2w + w2 = -6.44

Factor a perfect square on the left side:
(w + 0.6)(w + 0.6) = -6.44

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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