334=w(w+6)

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Solution for 334=w(w+6) equation:


Simplifying
334 = w(w + 6)

Reorder the terms:
334 = w(6 + w)
334 = (6 * w + w * w)
334 = (6w + w2)

Solving
334 = 6w + w2

Solving for variable 'w'.

Reorder the terms:
334 + -6w + -1w2 = 6w + -6w + w2 + -1w2

Combine like terms: 6w + -6w = 0
334 + -6w + -1w2 = 0 + w2 + -1w2
334 + -6w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
334 + -6w + -1w2 = 0

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

Divide each side by '-1'.
-334 + 6w + w2 = 0

Move the constant term to the right:

Add '334' to each side of the equation.
-334 + 6w + 334 + w2 = 0 + 334

Reorder the terms:
-334 + 334 + 6w + w2 = 0 + 334

Combine like terms: -334 + 334 = 0
0 + 6w + w2 = 0 + 334
6w + w2 = 0 + 334

Combine like terms: 0 + 334 = 334
6w + w2 = 334

The w term is 6w.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6w + 9 + w2 = 334 + 9

Reorder the terms:
9 + 6w + w2 = 334 + 9

Combine like terms: 334 + 9 = 343
9 + 6w + w2 = 343

Factor a perfect square on the left side:
(w + 3)(w + 3) = 343

Calculate the square root of the right side: 18.520259177

Break this problem into two subproblems by setting 
(w + 3) equal to 18.520259177 and -18.520259177.

Subproblem 1

w + 3 = 18.520259177 Simplifying w + 3 = 18.520259177 Reorder the terms: 3 + w = 18.520259177 Solving 3 + w = 18.520259177 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 18.520259177 + -3 Combine like terms: 3 + -3 = 0 0 + w = 18.520259177 + -3 w = 18.520259177 + -3 Combine like terms: 18.520259177 + -3 = 15.520259177 w = 15.520259177 Simplifying w = 15.520259177

Subproblem 2

w + 3 = -18.520259177 Simplifying w + 3 = -18.520259177 Reorder the terms: 3 + w = -18.520259177 Solving 3 + w = -18.520259177 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = -18.520259177 + -3 Combine like terms: 3 + -3 = 0 0 + w = -18.520259177 + -3 w = -18.520259177 + -3 Combine like terms: -18.520259177 + -3 = -21.520259177 w = -21.520259177 Simplifying w = -21.520259177

Solution

The solution to the problem is based on the solutions from the subproblems. w = {15.520259177, -21.520259177}

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