4w^2-14w+6=-38

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Solution for 4w^2-14w+6=-38 equation: 


Simplifying
4w2 + -14w + 6 = -38

Reorder the terms:
6 + -14w + 4w2 = -38

Solving
6 + -14w + 4w2 = -38

Solving for variable 'w'.

Reorder the terms:
6 + 38 + -14w + 4w2 = -38 + 38

Combine like terms: 6 + 38 = 44
44 + -14w + 4w2 = -38 + 38

Combine like terms: -38 + 38 = 0
44 + -14w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(22 + -7w + 2w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(22 + -7w + 2w2)' equal to zero and attempt to solve:

Simplifying
22 + -7w + 2w2 = 0

Solving
22 + -7w + 2w2 = 0

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

Divide each side by '2'.
11 + -3.5w + w2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -3.5w + -11 + w2 = 0 + -11

Reorder the terms:
11 + -11 + -3.5w + w2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3.5w + w2 = 0 + -11
-3.5w + w2 = 0 + -11

Combine like terms: 0 + -11 = -11
-3.5w + w2 = -11

The w term is -3.5w.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5w + 3.0625 + w2 = -11 + 3.0625

Reorder the terms:
3.0625 + -3.5w + w2 = -11 + 3.0625

Combine like terms: -11 + 3.0625 = -7.9375
3.0625 + -3.5w + w2 = -7.9375

Factor a perfect square on the left side:
(w + -1.75)(w + -1.75) = -7.9375

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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