2w^2-6w+20=2w-10

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Solution for 2w^2-6w+20=2w-10 equation: 


Simplifying
2w2 + -6w + 20 = 2w + -10

Reorder the terms:
20 + -6w + 2w2 = 2w + -10

Reorder the terms:
20 + -6w + 2w2 = -10 + 2w

Solving
20 + -6w + 2w2 = -10 + 2w

Solving for variable 'w'.

Reorder the terms:
20 + 10 + -6w + -2w + 2w2 = -10 + 2w + 10 + -2w

Combine like terms: 20 + 10 = 30
30 + -6w + -2w + 2w2 = -10 + 2w + 10 + -2w

Combine like terms: -6w + -2w = -8w
30 + -8w + 2w2 = -10 + 2w + 10 + -2w

Reorder the terms:
30 + -8w + 2w2 = -10 + 10 + 2w + -2w

Combine like terms: -10 + 10 = 0
30 + -8w + 2w2 = 0 + 2w + -2w
30 + -8w + 2w2 = 2w + -2w

Combine like terms: 2w + -2w = 0
30 + -8w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -4w + w2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + -4w + w2)' equal to zero and attempt to solve:

Simplifying
15 + -4w + w2 = 0

Solving
15 + -4w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -4w + -15 + w2 = 0 + -15

Reorder the terms:
15 + -15 + -4w + w2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -4w + w2 = 0 + -15
-4w + w2 = 0 + -15

Combine like terms: 0 + -15 = -15
-4w + w2 = -15

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 = -15 + 4

Reorder the terms:
4 + -4w + w2 = -15 + 4

Combine like terms: -15 + 4 = -11
4 + -4w + w2 = -11

Factor a perfect square on the left side:
(w + -2)(w + -2) = -11

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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