(4w^2+6w-8)-(9w^2+2w+5)=

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Solution for (4w^2+6w-8)-(9w^2+2w+5)= equation: 


Simplifying
(4w2 + 6w + -8) + -1(9w2 + 2w + 5) = 0

Reorder the terms:
(-8 + 6w + 4w2) + -1(9w2 + 2w + 5) = 0

Remove parenthesis around (-8 + 6w + 4w2)
-8 + 6w + 4w2 + -1(9w2 + 2w + 5) = 0

Reorder the terms:
-8 + 6w + 4w2 + -1(5 + 2w + 9w2) = 0
-8 + 6w + 4w2 + (5 * -1 + 2w * -1 + 9w2 * -1) = 0
-8 + 6w + 4w2 + (-5 + -2w + -9w2) = 0

Reorder the terms:
-8 + -5 + 6w + -2w + 4w2 + -9w2 = 0

Combine like terms: -8 + -5 = -13
-13 + 6w + -2w + 4w2 + -9w2 = 0

Combine like terms: 6w + -2w = 4w
-13 + 4w + 4w2 + -9w2 = 0

Combine like terms: 4w2 + -9w2 = -5w2
-13 + 4w + -5w2 = 0

Solving
-13 + 4w + -5w2 = 0

Solving for variable 'w'.

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

Divide each side by '-5'.
2.6 + -0.8w + w2 = 0

Move the constant term to the right:

Add '-2.6' to each side of the equation.
2.6 + -0.8w + -2.6 + w2 = 0 + -2.6

Reorder the terms:
2.6 + -2.6 + -0.8w + w2 = 0 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + -0.8w + w2 = 0 + -2.6
-0.8w + w2 = 0 + -2.6

Combine like terms: 0 + -2.6 = -2.6
-0.8w + w2 = -2.6

The w term is -0.8w.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8w + 0.16 + w2 = -2.6 + 0.16

Reorder the terms:
0.16 + -0.8w + w2 = -2.6 + 0.16

Combine like terms: -2.6 + 0.16 = -2.44
0.16 + -0.8w + w2 = -2.44

Factor a perfect square on the left side:
(w + -0.4)(w + -0.4) = -2.44

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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