34=w^2+2w

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Solution for 34=w^2+2w equation:


Simplifying
34 = w2 + 2w

Reorder the terms:
34 = 2w + w2

Solving
34 = 2w + w2

Solving for variable 'w'.

Reorder the terms:
34 + -2w + -1w2 = 2w + -2w + w2 + -1w2

Combine like terms: 2w + -2w = 0
34 + -2w + -1w2 = 0 + w2 + -1w2
34 + -2w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
34 + -2w + -1w2 = 0

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

Divide each side by '-1'.
-34 + 2w + w2 = 0

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + 2w + 34 + w2 = 0 + 34

Reorder the terms:
-34 + 34 + 2w + w2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + 2w + w2 = 0 + 34
2w + w2 = 0 + 34

Combine like terms: 0 + 34 = 34
2w + w2 = 34

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 34 + 1

Reorder the terms:
1 + 2w + w2 = 34 + 1

Combine like terms: 34 + 1 = 35
1 + 2w + w2 = 35

Factor a perfect square on the left side:
(w + 1)(w + 1) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(w + 1) equal to 5.916079783 and -5.916079783.

Subproblem 1

w + 1 = 5.916079783 Simplifying w + 1 = 5.916079783 Reorder the terms: 1 + w = 5.916079783 Solving 1 + w = 5.916079783 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = 5.916079783 + -1 Combine like terms: 1 + -1 = 0 0 + w = 5.916079783 + -1 w = 5.916079783 + -1 Combine like terms: 5.916079783 + -1 = 4.916079783 w = 4.916079783 Simplifying w = 4.916079783

Subproblem 2

w + 1 = -5.916079783 Simplifying w + 1 = -5.916079783 Reorder the terms: 1 + w = -5.916079783 Solving 1 + w = -5.916079783 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + w = -5.916079783 + -1 Combine like terms: 1 + -1 = 0 0 + w = -5.916079783 + -1 w = -5.916079783 + -1 Combine like terms: -5.916079783 + -1 = -6.916079783 w = -6.916079783 Simplifying w = -6.916079783

Solution

The solution to the problem is based on the solutions from the subproblems. w = {4.916079783, -6.916079783}

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