w^2+3w+4w^2+1=4w^2-5

Solution for w^2+3w+4w^2+1=4w^2-5 equation:

Simplifying
w2 + 3w + 4w2 + 1 = 4w2 + -5

Reorder the terms:
1 + 3w + w2 + 4w2 = 4w2 + -5

Combine like terms: w2 + 4w2 = 5w2
1 + 3w + 5w2 = 4w2 + -5

Reorder the terms:
1 + 3w + 5w2 = -5 + 4w2

Solving
1 + 3w + 5w2 = -5 + 4w2

Solving for variable 'w'.

Reorder the terms:
1 + 5 + 3w + 5w2 + -4w2 = -5 + 4w2 + 5 + -4w2

Combine like terms: 1 + 5 = 6
6 + 3w + 5w2 + -4w2 = -5 + 4w2 + 5 + -4w2

Combine like terms: 5w2 + -4w2 = 1w2
6 + 3w + 1w2 = -5 + 4w2 + 5 + -4w2

Reorder the terms:
6 + 3w + 1w2 = -5 + 5 + 4w2 + -4w2

Combine like terms: -5 + 5 = 0
6 + 3w + 1w2 = 0 + 4w2 + -4w2
6 + 3w + 1w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
6 + 3w + 1w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 3w + -6 + w2 = 0 + -6

Reorder the terms:
6 + -6 + 3w + w2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 3w + w2 = 0 + -6
3w + w2 = 0 + -6

Combine like terms: 0 + -6 = -6
3w + w2 = -6

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 = -6 + 2.25

Reorder the terms:
2.25 + 3w + w2 = -6 + 2.25

Combine like terms: -6 + 2.25 = -3.75
2.25 + 3w + w2 = -3.75

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.