(w+3)2=2w^2-4w+33

Solution for (w+3)2=2w^2-4w+33 equation:

Simplifying
(w + 3) * 2 = 2w2 + -4w + 33

Reorder the terms:
(3 + w) * 2 = 2w2 + -4w + 33

Reorder the terms for easier multiplication:
2(3 + w) = 2w2 + -4w + 33
(3 * 2 + w * 2) = 2w2 + -4w + 33
(6 + 2w) = 2w2 + -4w + 33

Reorder the terms:
6 + 2w = 33 + -4w + 2w2

Solving
6 + 2w = 33 + -4w + 2w2

Solving for variable 'w'.

Reorder the terms:
6 + -33 + 2w + 4w + -2w2 = 33 + -4w + 2w2 + -33 + 4w + -2w2

Combine like terms: 6 + -33 = -27
-27 + 2w + 4w + -2w2 = 33 + -4w + 2w2 + -33 + 4w + -2w2

Combine like terms: 2w + 4w = 6w
-27 + 6w + -2w2 = 33 + -4w + 2w2 + -33 + 4w + -2w2

Reorder the terms:
-27 + 6w + -2w2 = 33 + -33 + -4w + 4w + 2w2 + -2w2

Combine like terms: 33 + -33 = 0
-27 + 6w + -2w2 = 0 + -4w + 4w + 2w2 + -2w2
-27 + 6w + -2w2 = -4w + 4w + 2w2 + -2w2

Combine like terms: -4w + 4w = 0
-27 + 6w + -2w2 = 0 + 2w2 + -2w2
-27 + 6w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-27 + 6w + -2w2 = 0

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

Divide each side by '-2'.
13.5 + -3w + w2 = 0

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + -3w + -13.5 + w2 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + -3w + w2 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + -3w + w2 = 0 + -13.5
-3w + w2 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
-3w + w2 = -13.5

The w term is -3w.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3w + 2.25 + w2 = -13.5 + 2.25

Reorder the terms:
2.25 + -3w + w2 = -13.5 + 2.25

Combine like terms: -13.5 + 2.25 = -11.25
2.25 + -3w + w2 = -11.25

Factor a perfect square on the left side:
(w + -1.5)(w + -1.5) = -11.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.