3w^2-24w+16=0

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Solution for 3w^2-24w+16=0 equation:


Simplifying
3w2 + -24w + 16 = 0

Reorder the terms:
16 + -24w + 3w2 = 0

Solving
16 + -24w + 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'.
5.333333333 + -8w + w2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -8w + -5.333333333 + w2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -8w + w2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -8w + w2 = 0 + -5.333333333
-8w + w2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-8w + w2 = -5.333333333

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 = -5.333333333 + 16

Reorder the terms:
16 + -8w + w2 = -5.333333333 + 16

Combine like terms: -5.333333333 + 16 = 10.666666667
16 + -8w + w2 = 10.666666667

Factor a perfect square on the left side:
(w + -4)(w + -4) = 10.666666667

Calculate the square root of the right side: 3.265986324

Break this problem into two subproblems by setting 
(w + -4) equal to 3.265986324 and -3.265986324.

Subproblem 1

w + -4 = 3.265986324 Simplifying w + -4 = 3.265986324 Reorder the terms: -4 + w = 3.265986324 Solving -4 + w = 3.265986324 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 = 3.265986324 + 4 Combine like terms: -4 + 4 = 0 0 + w = 3.265986324 + 4 w = 3.265986324 + 4 Combine like terms: 3.265986324 + 4 = 7.265986324 w = 7.265986324 Simplifying w = 7.265986324

Subproblem 2

w + -4 = -3.265986324 Simplifying w + -4 = -3.265986324 Reorder the terms: -4 + w = -3.265986324 Solving -4 + w = -3.265986324 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 = -3.265986324 + 4 Combine like terms: -4 + 4 = 0 0 + w = -3.265986324 + 4 w = -3.265986324 + 4 Combine like terms: -3.265986324 + 4 = 0.734013676 w = 0.734013676 Simplifying w = 0.734013676

Solution

The solution to the problem is based on the solutions from the subproblems. w = {7.265986324, 0.734013676}

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