2w^2-10w-40=0

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Solution for 2w^2-10w-40=0 equation: 


Simplifying
2w2 + -10w + -40 = 0

Reorder the terms:
-40 + -10w + 2w2 = 0

Solving
-40 + -10w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -5w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-20 + -5w + w2)' equal to zero and attempt to solve:

Simplifying
-20 + -5w + w2 = 0

Solving
-20 + -5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -5w + 20 + w2 = 0 + 20

Reorder the terms:
-20 + 20 + -5w + w2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -5w + w2 = 0 + 20
-5w + w2 = 0 + 20

Combine like terms: 0 + 20 = 20
-5w + w2 = 20

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 = 20 + 6.25

Reorder the terms:
6.25 + -5w + w2 = 20 + 6.25

Combine like terms: 20 + 6.25 = 26.25
6.25 + -5w + w2 = 26.25

Factor a perfect square on the left side:
(w + -2.5)(w + -2.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(w + -2.5) equal to 5.123475383 and -5.123475383.


Subproblem 1
w + -2.5 = 5.123475383

Simplifying
w + -2.5 = 5.123475383

Reorder the terms:
-2.5 + w = 5.123475383

Solving
-2.5 + w = 5.123475383

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 = 5.123475383 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + w = 5.123475383 + 2.5
w = 5.123475383 + 2.5

Combine like terms: 5.123475383 + 2.5 = 7.623475383
w = 7.623475383

Simplifying
w = 7.623475383


Subproblem 2
w + -2.5 = -5.123475383

Simplifying
w + -2.5 = -5.123475383

Reorder the terms:
-2.5 + w = -5.123475383

Solving
-2.5 + w = -5.123475383

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 = -5.123475383 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + w = -5.123475383 + 2.5
w = -5.123475383 + 2.5

Combine like terms: -5.123475383 + 2.5 = -2.623475383
w = -2.623475383

Simplifying
w = -2.623475383


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.623475383, -2.623475383}
Solution
w = {7.623475383, -2.623475383}

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