324-3w-w^2=0

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Solution for 324-3w-w^2=0 equation:


Simplifying
324 + -3w + -1w2 = 0

Solving
324 + -3w + -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'.
-324 + 3w + w2 = 0

Move the constant term to the right:

Add '324' to each side of the equation.
-324 + 3w + 324 + w2 = 0 + 324

Reorder the terms:
-324 + 324 + 3w + w2 = 0 + 324

Combine like terms: -324 + 324 = 0
0 + 3w + w2 = 0 + 324
3w + w2 = 0 + 324

Combine like terms: 0 + 324 = 324
3w + w2 = 324

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 324 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 324 + 2.25

Combine like terms: 324 + 2.25 = 326.25
2.25 + 3w + w2 = 326.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 326.25

Calculate the square root of the right side: 18.062391868

Break this problem into two subproblems by setting 
(w + 1.5) equal to 18.062391868 and -18.062391868.

Subproblem 1

w + 1.5 = 18.062391868 Simplifying w + 1.5 = 18.062391868 Reorder the terms: 1.5 + w = 18.062391868 Solving 1.5 + w = 18.062391868 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = 18.062391868 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = 18.062391868 + -1.5 w = 18.062391868 + -1.5 Combine like terms: 18.062391868 + -1.5 = 16.562391868 w = 16.562391868 Simplifying w = 16.562391868

Subproblem 2

w + 1.5 = -18.062391868 Simplifying w + 1.5 = -18.062391868 Reorder the terms: 1.5 + w = -18.062391868 Solving 1.5 + w = -18.062391868 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + w = -18.062391868 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + w = -18.062391868 + -1.5 w = -18.062391868 + -1.5 Combine like terms: -18.062391868 + -1.5 = -19.562391868 w = -19.562391868 Simplifying w = -19.562391868

Solution

The solution to the problem is based on the solutions from the subproblems. w = {16.562391868, -19.562391868}

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