(-2w^2+4w-7)+(3w^2+6w+5)=

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Solution for (-2w^2+4w-7)+(3w^2+6w+5)= equation:


Simplifying
(-2w2 + 4w + -7) + (3w2 + 6w + 5) = 0

Reorder the terms:
(-7 + 4w + -2w2) + (3w2 + 6w + 5) = 0

Remove parenthesis around (-7 + 4w + -2w2)
-7 + 4w + -2w2 + (3w2 + 6w + 5) = 0

Reorder the terms:
-7 + 4w + -2w2 + (5 + 6w + 3w2) = 0

Remove parenthesis around (5 + 6w + 3w2)
-7 + 4w + -2w2 + 5 + 6w + 3w2 = 0

Reorder the terms:
-7 + 5 + 4w + 6w + -2w2 + 3w2 = 0

Combine like terms: -7 + 5 = -2
-2 + 4w + 6w + -2w2 + 3w2 = 0

Combine like terms: 4w + 6w = 10w
-2 + 10w + -2w2 + 3w2 = 0

Combine like terms: -2w2 + 3w2 = 1w2
-2 + 10w + 1w2 = 0

Solving
-2 + 10w + 1w2 = 0

Solving for variable 'w'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 10w + 2 + w2 = 0 + 2

Reorder the terms:
-2 + 2 + 10w + w2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 10w + w2 = 0 + 2
10w + w2 = 0 + 2

Combine like terms: 0 + 2 = 2
10w + w2 = 2

The w term is 10w.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10w + 25 + w2 = 2 + 25

Reorder the terms:
25 + 10w + w2 = 2 + 25

Combine like terms: 2 + 25 = 27
25 + 10w + w2 = 27

Factor a perfect square on the left side:
(w + 5)(w + 5) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(w + 5) equal to 5.196152423 and -5.196152423.

Subproblem 1

w + 5 = 5.196152423 Simplifying w + 5 = 5.196152423 Reorder the terms: 5 + w = 5.196152423 Solving 5 + w = 5.196152423 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 5.196152423 + -5 Combine like terms: 5 + -5 = 0 0 + w = 5.196152423 + -5 w = 5.196152423 + -5 Combine like terms: 5.196152423 + -5 = 0.196152423 w = 0.196152423 Simplifying w = 0.196152423

Subproblem 2

w + 5 = -5.196152423 Simplifying w + 5 = -5.196152423 Reorder the terms: 5 + w = -5.196152423 Solving 5 + w = -5.196152423 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = -5.196152423 + -5 Combine like terms: 5 + -5 = 0 0 + w = -5.196152423 + -5 w = -5.196152423 + -5 Combine like terms: -5.196152423 + -5 = -10.196152423 w = -10.196152423 Simplifying w = -10.196152423

Solution

The solution to the problem is based on the solutions from the subproblems. w = {0.196152423, -10.196152423}

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