(-4w^2+w-5)+(2w^2+7w+6)=

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Solution for (-4w^2+w-5)+(2w^2+7w+6)= equation:


Simplifying
(-4w2 + w + -5) + (2w2 + 7w + 6) = 0

Reorder the terms:
(-5 + w + -4w2) + (2w2 + 7w + 6) = 0

Remove parenthesis around (-5 + w + -4w2)
-5 + w + -4w2 + (2w2 + 7w + 6) = 0

Reorder the terms:
-5 + w + -4w2 + (6 + 7w + 2w2) = 0

Remove parenthesis around (6 + 7w + 2w2)
-5 + w + -4w2 + 6 + 7w + 2w2 = 0

Reorder the terms:
-5 + 6 + w + 7w + -4w2 + 2w2 = 0

Combine like terms: -5 + 6 = 1
1 + w + 7w + -4w2 + 2w2 = 0

Combine like terms: w + 7w = 8w
1 + 8w + -4w2 + 2w2 = 0

Combine like terms: -4w2 + 2w2 = -2w2
1 + 8w + -2w2 = 0

Solving
1 + 8w + -2w2 = 0

Solving for variable 'w'.

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

Divide each side by '-2'.
-0.5 + -4w + w2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -4w + 0.5 + w2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -4w + w2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -4w + w2 = 0 + 0.5
-4w + w2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-4w + w2 = 0.5

The w term is -4w.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4w + 4 + w2 = 0.5 + 4

Reorder the terms:
4 + -4w + w2 = 0.5 + 4

Combine like terms: 0.5 + 4 = 4.5
4 + -4w + w2 = 4.5

Factor a perfect square on the left side:
(w + -2)(w + -2) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(w + -2) equal to 2.121320344 and -2.121320344.

Subproblem 1

w + -2 = 2.121320344 Simplifying w + -2 = 2.121320344 Reorder the terms: -2 + w = 2.121320344 Solving -2 + w = 2.121320344 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 2.121320344 + 2 Combine like terms: -2 + 2 = 0 0 + w = 2.121320344 + 2 w = 2.121320344 + 2 Combine like terms: 2.121320344 + 2 = 4.121320344 w = 4.121320344 Simplifying w = 4.121320344

Subproblem 2

w + -2 = -2.121320344 Simplifying w + -2 = -2.121320344 Reorder the terms: -2 + w = -2.121320344 Solving -2 + w = -2.121320344 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = -2.121320344 + 2 Combine like terms: -2 + 2 = 0 0 + w = -2.121320344 + 2 w = -2.121320344 + 2 Combine like terms: -2.121320344 + 2 = -0.121320344 w = -0.121320344 Simplifying w = -0.121320344

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.121320344, -0.121320344}

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