(-7w^2+5w-1)+(6w^2+3w+4)=

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Solution for (-7w^2+5w-1)+(6w^2+3w+4)= equation:


Simplifying
(-7w2 + 5w + -1) + (6w2 + 3w + 4) = 0

Reorder the terms:
(-1 + 5w + -7w2) + (6w2 + 3w + 4) = 0

Remove parenthesis around (-1 + 5w + -7w2)
-1 + 5w + -7w2 + (6w2 + 3w + 4) = 0

Reorder the terms:
-1 + 5w + -7w2 + (4 + 3w + 6w2) = 0

Remove parenthesis around (4 + 3w + 6w2)
-1 + 5w + -7w2 + 4 + 3w + 6w2 = 0

Reorder the terms:
-1 + 4 + 5w + 3w + -7w2 + 6w2 = 0

Combine like terms: -1 + 4 = 3
3 + 5w + 3w + -7w2 + 6w2 = 0

Combine like terms: 5w + 3w = 8w
3 + 8w + -7w2 + 6w2 = 0

Combine like terms: -7w2 + 6w2 = -1w2
3 + 8w + -1w2 = 0

Solving
3 + 8w + -1w2 = 0

Solving for variable 'w'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + -8w + w2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -8w + 3 + w2 = 0 + 3

Reorder the terms:
-3 + 3 + -8w + w2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8w + w2 = 0 + 3
-8w + w2 = 0 + 3

Combine like terms: 0 + 3 = 3
-8w + w2 = 3

The w term is -8w.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8w + 16 + w2 = 3 + 16

Reorder the terms:
16 + -8w + w2 = 3 + 16

Combine like terms: 3 + 16 = 19
16 + -8w + w2 = 19

Factor a perfect square on the left side:
(w + -4)(w + -4) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(w + -4) equal to 4.358898944 and -4.358898944.

Subproblem 1

w + -4 = 4.358898944 Simplifying w + -4 = 4.358898944 Reorder the terms: -4 + w = 4.358898944 Solving -4 + w = 4.358898944 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + w = 4.358898944 + 4 w = 4.358898944 + 4 Combine like terms: 4.358898944 + 4 = 8.358898944 w = 8.358898944 Simplifying w = 8.358898944

Subproblem 2

w + -4 = -4.358898944 Simplifying w + -4 = -4.358898944 Reorder the terms: -4 + w = -4.358898944 Solving -4 + w = -4.358898944 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = -4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + w = -4.358898944 + 4 w = -4.358898944 + 4 Combine like terms: -4.358898944 + 4 = -0.358898944 w = -0.358898944 Simplifying w = -0.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. w = {8.358898944, -0.358898944}

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