8(8-k)=-2k(k-5)

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Solution for 8(8-k)=-2k(k-5) equation: 


Simplifying
8(8 + -1k) = -2k(k + -5)
(8 * 8 + -1k * 8) = -2k(k + -5)
(64 + -8k) = -2k(k + -5)

Reorder the terms:
64 + -8k = -2k(-5 + k)
64 + -8k = (-5 * -2k + k * -2k)
64 + -8k = (10k + -2k2)

Solving
64 + -8k = 10k + -2k2

Solving for variable 'k'.

Combine like terms: -8k + -10k = -18k
64 + -18k + 2k2 = 10k + -2k2 + -10k + 2k2

Reorder the terms:
64 + -18k + 2k2 = 10k + -10k + -2k2 + 2k2

Combine like terms: 10k + -10k = 0
64 + -18k + 2k2 = 0 + -2k2 + 2k2
64 + -18k + 2k2 = -2k2 + 2k2

Combine like terms: -2k2 + 2k2 = 0
64 + -18k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(32 + -9k + k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(32 + -9k + k2)' equal to zero and attempt to solve:

Simplifying
32 + -9k + k2 = 0

Solving
32 + -9k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -9k + -32 + k2 = 0 + -32

Reorder the terms:
32 + -32 + -9k + k2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -9k + k2 = 0 + -32
-9k + k2 = 0 + -32

Combine like terms: 0 + -32 = -32
-9k + k2 = -32

The k term is -9k.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9k + 20.25 + k2 = -32 + 20.25

Reorder the terms:
20.25 + -9k + k2 = -32 + 20.25

Combine like terms: -32 + 20.25 = -11.75
20.25 + -9k + k2 = -11.75

Factor a perfect square on the left side:
(k + -4.5)(k + -4.5) = -11.75

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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