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

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


Simplifying
(1w2 + 5w + -7) + (2w2 + 3w + 6) = 0

Reorder the terms:
(-7 + 5w + 1w2) + (2w2 + 3w + 6) = 0

Remove parenthesis around (-7 + 5w + 1w2)
-7 + 5w + 1w2 + (2w2 + 3w + 6) = 0

Reorder the terms:
-7 + 5w + 1w2 + (6 + 3w + 2w2) = 0

Remove parenthesis around (6 + 3w + 2w2)
-7 + 5w + 1w2 + 6 + 3w + 2w2 = 0

Reorder the terms:
-7 + 6 + 5w + 3w + 1w2 + 2w2 = 0

Combine like terms: -7 + 6 = -1
-1 + 5w + 3w + 1w2 + 2w2 = 0

Combine like terms: 5w + 3w = 8w
-1 + 8w + 1w2 + 2w2 = 0

Combine like terms: 1w2 + 2w2 = 3w2
-1 + 8w + 3w2 = 0

Solving
-1 + 8w + 3w2 = 0

Solving for variable 'w'.

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

Divide each side by '3'.
-0.3333333333 + 2.666666667w + w2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 2.666666667w + 0.3333333333 + w2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 2.666666667w + w2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 2.666666667w + w2 = 0 + 0.3333333333
2.666666667w + w2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
2.666666667w + w2 = 0.3333333333

The w term is 2.666666667w.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667w + 1.777777780 + w2 = 0.3333333333 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667w + w2 = 0.3333333333 + 1.777777780

Combine like terms: 0.3333333333 + 1.777777780 = 2.1111111133
1.777777780 + 2.666666667w + w2 = 2.1111111133

Factor a perfect square on the left side:
(w + 1.333333334)(w + 1.333333334) = 2.1111111133

Calculate the square root of the right side: 1.452966315

Break this problem into two subproblems by setting 
(w + 1.333333334) equal to 1.452966315 and -1.452966315.

Subproblem 1

w + 1.333333334 = 1.452966315 Simplifying w + 1.333333334 = 1.452966315 Reorder the terms: 1.333333334 + w = 1.452966315 Solving 1.333333334 + w = 1.452966315 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + w = 1.452966315 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + w = 1.452966315 + -1.333333334 w = 1.452966315 + -1.333333334 Combine like terms: 1.452966315 + -1.333333334 = 0.119632981 w = 0.119632981 Simplifying w = 0.119632981

Subproblem 2

w + 1.333333334 = -1.452966315 Simplifying w + 1.333333334 = -1.452966315 Reorder the terms: 1.333333334 + w = -1.452966315 Solving 1.333333334 + w = -1.452966315 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + w = -1.452966315 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + w = -1.452966315 + -1.333333334 w = -1.452966315 + -1.333333334 Combine like terms: -1.452966315 + -1.333333334 = -2.786299649 w = -2.786299649 Simplifying w = -2.786299649

Solution

The solution to the problem is based on the solutions from the subproblems. w = {0.119632981, -2.786299649}

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