2w^2+8w-270=0

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Solution for 2w^2+8w-270=0 equation:


Simplifying
2w2 + 8w + -270 = 0

Reorder the terms:
-270 + 8w + 2w2 = 0

Solving
-270 + 8w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-135 + 4w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-135 + 4w + w2)' equal to zero and attempt to solve:

Simplifying
-135 + 4w + w2 = 0

Solving
-135 + 4w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '135' to each side of the equation.
-135 + 4w + 135 + w2 = 0 + 135

Reorder the terms:
-135 + 135 + 4w + w2 = 0 + 135

Combine like terms: -135 + 135 = 0
0 + 4w + w2 = 0 + 135
4w + w2 = 0 + 135

Combine like terms: 0 + 135 = 135
4w + w2 = 135

The w term is 4w.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4w + 4 + w2 = 135 + 4

Reorder the terms:
4 + 4w + w2 = 135 + 4

Combine like terms: 135 + 4 = 139
4 + 4w + w2 = 139

Factor a perfect square on the left side:
(w + 2)(w + 2) = 139

Calculate the square root of the right side: 11.789826123

Break this problem into two subproblems by setting 
(w + 2) equal to 11.789826123 and -11.789826123.


Subproblem 1
w + 2 = 11.789826123

Simplifying
w + 2 = 11.789826123

Reorder the terms:
2 + w = 11.789826123

Solving
2 + w = 11.789826123

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = 11.789826123 + -2

Combine like terms: 2 + -2 = 0
0 + w = 11.789826123 + -2
w = 11.789826123 + -2

Combine like terms: 11.789826123 + -2 = 9.789826123
w = 9.789826123

Simplifying
w = 9.789826123


Subproblem 2
w + 2 = -11.789826123

Simplifying
w + 2 = -11.789826123

Reorder the terms:
2 + w = -11.789826123

Solving
2 + w = -11.789826123

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + w = -11.789826123 + -2

Combine like terms: 2 + -2 = 0
0 + w = -11.789826123 + -2
w = -11.789826123 + -2

Combine like terms: -11.789826123 + -2 = -13.789826123
w = -13.789826123

Simplifying
w = -13.789826123


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {9.789826123, -13.789826123}
Solution
w = {9.789826123, -13.789826123}

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