3w^2-15w-12=0

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Solution for 3w^2-15w-12=0 equation: 


Simplifying
3w2 + -15w + -12 = 0

Reorder the terms:
-12 + -15w + 3w2 = 0

Solving
-12 + -15w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -5w + w2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -5w + w2)' equal to zero and attempt to solve:

Simplifying
-4 + -5w + w2 = 0

Solving
-4 + -5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -5w + 4 + w2 = 0 + 4

Reorder the terms:
-4 + 4 + -5w + w2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5w + w2 = 0 + 4
-5w + w2 = 0 + 4

Combine like terms: 0 + 4 = 4
-5w + w2 = 4

The w term is -5w.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5w + 6.25 + w2 = 4 + 6.25

Reorder the terms:
6.25 + -5w + w2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + -5w + w2 = 10.25

Factor a perfect square on the left side:
(w + -2.5)(w + -2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(w + -2.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
w + -2.5 = 3.201562119

Simplifying
w + -2.5 = 3.201562119

Reorder the terms:
-2.5 + w = 3.201562119

Solving
-2.5 + w = 3.201562119

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + w = 3.201562119 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + w = 3.201562119 + 2.5
w = 3.201562119 + 2.5

Combine like terms: 3.201562119 + 2.5 = 5.701562119
w = 5.701562119

Simplifying
w = 5.701562119


Subproblem 2
w + -2.5 = -3.201562119

Simplifying
w + -2.5 = -3.201562119

Reorder the terms:
-2.5 + w = -3.201562119

Solving
-2.5 + w = -3.201562119

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + w = -3.201562119 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + w = -3.201562119 + 2.5
w = -3.201562119 + 2.5

Combine like terms: -3.201562119 + 2.5 = -0.701562119
w = -0.701562119

Simplifying
w = -0.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.701562119, -0.701562119}
Solution
w = {5.701562119, -0.701562119}

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